Who "invented" flying saucers?

Specifically, who created the idea that aliens would travel in saucer-like vehicles?

As to who created the idea, it’s hard to say. As far as the term “Flying Saucer” goes, I think it was an invention of the press in response to Kenneth Arnold’s Mt. Rainier UFO sighting in 1947. Arnold described the things he saw as looking like disks or saucers.

Right, and after Arnold there were many copycat sightings.
Charles Fort wrote about many strange things in the sky, but IIRC they were usually cigar shaped, not sausage shaped. The great airship mystery of the 1890s (which concerned human piloted craft) were all cigar shaped also.

See the second paragraph here: Flying saucer - Wikipedia

There were already science fiction images from the pulps depicting disc-shaped craft (although rarely as simple as the stereotypical “flying saucer” – they tended to be studded with ornate knobs and portholes). A recent article in Skeptical Inquirer reprints several such illustrations. In addition, guys like Raymond Palmer printed pieces about disc-shaped alien craft.
As noted above and in the cites given, it was Kenneth Arnold’s 1947 sighting near Mt. Rainier that launched “Flying saucers” officially, although originally described the items as sort of boomerand-shaped. It was their* motion* that was “like a saucer skipping across the water”> Nevertheless, people latched onto the idea of saucer-shaped objects. Later on, when Arnold re-told his story (in Palmer’s magazine, Fate), he called them saucer-shaped, and they were so depicted on the cover.
Science fiction film moved in to cement the idea. There was a film Flying Saucer by 1950. When the made the movie The Day the Earth Stood Still, Klaatu used a featureless flying saucer, even though the original story “Farewell to the Master” described the craft as “ovoid”. Similarly, in The Thing (from Another World) the cfraft is shown to be a flying saucer, although in Campbell’s original story “Who Goes There?” it is described as shaped “like a submarine”. And in This Island Earth the Metalunans fly in a palatial flying saucer, although in Raymond F. Jones’ original novel the ship is, again, ovoid.
Then came Forbidden Planet with its human flying saucer, and Earth Vs. the Flying Saucers, and lots of other movies and TV shows that used the idea. People were accultured to the idea, and, besides, optical phenomena mistaken for such UFOs often are basically dots, which can easily be interpreted as circular saucers

Depending on how much you want to stretch the word, apparently the first use of the word saucer with a UFO sighting took place in Texas in 1878. The story, such as it is, is reported in The Real Cowboys & Aliens, 2nd Edition: UFO Encounters of the Old West, by Noe Torres and John LeMay.

Chapter 3 is called “The Farmer and the Flying Saucer,” the tale of John Martin who saw a dark object in the sky on January 2, 1878. If you read the account carefully, however, he described the object as sort of like a balloon. It was the newspaper who said it was the size of a “large saucer,” which could mean anything.

The chapter also includes a picture of a flying saucer captioned “Double Disk sighting in 1927.” It has nothing to do with the chapter or the book, but it’s credited to UFOcasebook.com so it probably the second image on this page, which is as flying saucerish as you could want. And looks even phonier when you click on it to see the whole image. There are a couple of other saucers on that page earlier than 1947 for those who believe.

The idea of a disk-shaped space craft has the rather intuitive appeal that it would be spinning, frisbee-like, thus generating artificial gravity inside.

Similarly, early sci-fi typically pictured a space station as being toroidal (doughnut-shaped) and rotating, again to provide artificial gravity.

I’ve never had the impression, or gotten the impression that other’s have the impression, that the spin of flying saucers is generating artificial gravity. Lots of flying saucer imagery has non-spinning saucers and most of the rest of what I recall has living accomodations that are oriented according to how the saucer will be at rest.
It may be intiuitive to you, but it doesn’t appear to be part of the mainstream understanding of saucery.

As CalMeacham mentioned above, the whole concept of flying saucers stems from a misinterpretation of one if the earliest sightings to gain media attention. Kenneth Arnold’s description of the craft he claimed to have seen was anything but saucer-shaped, but he said the motion was skipping up and down “like a saucer would if you skipped it across water”. (Which I always found odd because who the hell skips saucers across water? Stones, yes, but not china!)

Anyway it seems the appeal of the phrase “flying saucer” was so great that it even coloured Arnold’s later memory of the event.

I suspect that it wasn’t just repretition of the phrase “flying saucers”, but also Ray Palmer pushing the concept of flying disks. as i mentioned, he’s the one who published Arnold’s later, longer account in Fate #1, but Palmer had also published some of those Sf magazines with disc-shaped craft on them. (It was claimed in 1983 that the Palmer-edited “Shaver Mystery” pieces depicted disc-shaped craft, in an article entitled, as if in answer to the OP’s question, Palmer was “The Man Who Invented Flying Saucers”. UFO skeptic Jerome Clark claims it ain’t so, and the Shaver craft were never depicted as discs. I haven’t read the original stories, so I can’t say. See here: Richard Sharpe Shaver - Wikipedia ). I have to disagree about Palmer’s influence being negligible – Fate was on a lot of newsstands.

Here’s the cover of Fate #1, by the way. I passed up a chance to buy an issue several years ago, and wish I hadn’t:

http://images.search.yahoo.com/images/view;_ylt=A0PDoTDmdlBQtTEAKLWJzbkF;_ylu=X3oDMTBlMTQ4cGxyBHNlYwNzcgRzbGsDaW1n?back=http%3A%2F%2Fimages.search.yahoo.com%2Fsearch%2Fimages%3Fp%3DShaver%2BMystery%26_adv_prop%3Dimage%26va%3DShaver%2BMystery%26fr%3Dyfp-t-701%26tab%3Dorganic%26ri%3D66&w=400&h=468&imgurl=www.thelivingmoon.com%2F49ufo_files%2F04images%2FKennith_Arnold%2Ffate1.jpg&rurl=http%3A%2F%2Fwww.thelivingmoon.com%2F49ufo_files%2F03files2%2F1945_Ray_Palmer.html&size=119.4+KB&name=The+Shaver+Mystery+was+born&p=Shaver+Mystery&oid=ba2121be47fb9b931c8b998c89ee02f9&fr2=&fr=yfp-t-701&tt=The%2BShaver%2BMystery%2Bwas%2Bborn&b=59&ni=200&no=66&ts=&tab=organic&sigr=126jhoppr&sigb=13uiba3ib&sigi=1232dljkg&.crumb=G.kSrW0OssH

Interesting topic-what made the USAF think that a flying saucer/disc would be a good design for a combat aircraft? A development contract was awarded to AVRO (Canada), and a prototype was built.
It didn’t work.

I don’t know about who thought discs would be good shapes, or why. Certainly we now have the example of the Frisbee as a stable spinning, flying disc, but that’s relatively recentm, as far as I know. Discus throwing is an ancient sport, but those ancie nt discs were huge, heavy chunks of shaped stone (I’ve seen one in a museum) – they had no lift at all. The Wikipedia website tells of a couple who started selling flying discs as early as 1938 in California. But the name of the Frisbee comes from “Frisby”, a bakery in Connecticut where students apparently discovered on their own that the pie tins could be “flown”. *I haven’t
researched the history of such discs mysaelf, but I’d be surprised if they went much farther back than the 1930s.

In any event, frsibees are interest in their aerodynamics. the spin definitely imparts stability. We studied this in one of my college physics classes. This isa distinct from spinning to produce artificial gravity. However, flying saucers are almost never depictedin film as spinning, and I don’;t know of any cases where reported UFOs are said to do this (The only cases in film being Ray Harryhausen’s Earth Vs. the Flying Saucers and Tim Burton’s fim Mars Attacks!, in which the saucers are clearly based on Harryhausen’s, rather than those fromthe original trading cards. In both cases, it seems to be only the outer shel that rotates – the inner ship appears to be stationary.)
One appeal of “flying saucers” (ironically, given their origin and propagation) is that they fulfill editor John Campbell’s criterion for good science fiction – they are alien devices that are as good as human things, but are very different fro m human constructions. Nobody had disc-shaped space ships. Despite the disc-shaped ships on some SF book covers, most space ships tended toward the cuigar-shaped. And practical human rocketry was all cigar-like. Saucers were exotic and different, even if they didn’t use spin to stabilize themselves. When Forbidden Planet finally put human beinghs in a saucer, rather than aliens, in the first movie to have faster-than-light travel, it was an epiphany. Cigar-shaped ships would still dominate, but if you really wanted to be futuristic you put people in a flying saucer. Twilight Zone did this for many years (often re-using clips from Forbidden Planet, which their production company had rights to), but Star Trek really brought it to public attention, with their flying saucer-like main hull.

*I assume that Robert Zemeckis was using a bit of literary license in putting the Connecticut-based Frisby tin in the hands of Marty McFly in 19th century California in Back to the Future III, probably before they even existed, but it was in a good cause.