I’ve got a vocal range of about a half an octave. If I ever get brave enough to do karaoke, what is a classic pop/rock/folk tune with a super small vocal range?
Cat’s in the Cradle is a fairly narrow range.
The question is, where is your range? I can recommend some for a low female/high male… but I can think of others in other ranges.
That would work. I kind of sound like Pavarotti if he got kicked in the nuts.
Can you get a couple of backup singers and do “Big Bad John” by Jimmy Dean? Jimmy’s vocal stylings lean more toward “talking” than “singing”, really. Still a good song.
“At the bottom of this mine lies a big, big man.”
Tubthumping (a song that I deeply hate, but never mind) is sung all within about 6 notes, and the majority of the song is two notes within a semitone of each other. Hard to do better than that 
Anything written for the leads in “My Fair Lady” or “Camelot.” Or anything by Tom Waits.
I’m no music expert, so i don’t know what its actual note spread is, but one crowd-pleaser that my limited vocal range can cope with is Neil Diamond’s Sweet Caroline.
How about “Take a Walk On the Wild Side” sung by Lou Reed?
The B-52’s is almost speaking, you need perfect timing though
It may be a small range, but not many can hit those notes at all without sounding like a complete tool.
My tiny little range can always handle Patti Smith songs. I usually do Because the Night or Gloria.
Are Madness popular in America? Their songs are pretty easy to sing; sometimes you have to go really fast, but if your voice is neither particularly low or high and your range is small, then they’re a good shot.
These Boots Are Made For Walking is a very easy song that’s available at most karaoke venues.
The Devil Went Down to Georgia is one of my staple Karaoke songs just because of the limited vocal range - I’m not much of a singer.
Anything written for Shania Twain.
I’ll usually go with Radiohead - Creep, though it depends on how deep your half an octave is. Ghost Riders in the Sky (the Johnny Cash version) is kinda fair game too.
Of course with karaoke it’s really best to either be a really solid singer or just completely suck and have fun with it. It’s the people who are “kinda close to sorta good” that seem lame. But if you wanna belt out I just don’t know what to do with myself a la Cameron Diaz in My Best Friend’s Wedding, go crazy 
“Ring of Fire.” It’s the perfect karaoke song.
“The roof…the roof…the roof is on fire”
Bloodhound Gang 
Anything written for Ringo Starr: “With a Little Help From My Friends”, “Octopus’s Garden”, “Yellow Submarine”, etc… John and Paul had to write songs specially for him because he didn’t have much range.