Our two year old has one of those ubiquitous toy xylophones that every child has at some point. It’s eight notes (one single scale) and kinda fun to dink around on, but I’m sick of playing nursery rhyme songs. I can play “Do Re Mi” from Sound of Music but I’d like to find some other fun songs. Obviously, w/ only eight notes to use, my options are limited, but I’m hoping some of you more musically inclined dopers could give me some ideas.
I can almost play “Joy to the World”–the Christmas Carol. (I have to admit, I’m not entirely sure whether it’s almost because I can’t remember the tune or because I run out of notes. Hmm, looks like it should work ok (yes, I checked a hymnal to confirm the tune.))
You can play practically anything in a major key, as long as there are no accidentals.
Well, many songs are going to dip beyond the eight-note range of the xylophone in question. I suppose if octave doesn’t matter to you, you can fake it, but, something common like low C-B-C isn’t going to be possible with that missing low B.
Loreena’s McKennitt’s version of Prospero’s Speech.
Good King Wencelas (however the hell you spell it).
Ode to Joy.
I think you can play The Huron Carol, but I’m not sure.
Amazing Grace.
I also have a toddler, and a xylophone. We have two recorders, too, which are I think nine notes, not an octave.
That was going to be my suggestion. You can play the melody all the way through, starting on E, except you have to cheat by playing the G in bar 12 up an octave. Still sounds good that way.
“Everyday”, Buddy Holly
The melody from “Close Encounters of the 3rd Kind” - but you might need a glass of water as well.
Anything by Beethoven. Linus could do it on a toy piano that only had the black keys painted on. You can do it on a xylophone.
It they can do8 bit Depeche Modeyou can do it on your xylo.
I know you can play the “Alphabet Song” because I figured that out when I was about four or five. My mother heard, and for most of my childhood she insisted that I become a musician. (She didn’t realize that I was actually saying I wanted to be a writer.)
If it’s morning, you can play “Reveille” and at night you can play “Taps.”
You’ll need another mallet (or a reasonable substitute) and can rock out with “Chopsticks”.
Also you can impress people with the melody of “Country Gardens”.
Here’s the youtube linkif you’re not familiar.
“Happy Birthday to You.”
Beastie Boys, “Girls.” Maybe not what you wanted? 
ETA: Hmm…on second listen, I think I hear a few accidentals in there.
Well that clip is much better but now you would need another xylophone, eh?
“With A Little Help From My Friends” - starts on E. Written for Ringo to sing, which is why it doesn’t go outside the octave.
You meant Schroeder, of course. 
You can also play “Twinkle, Twinkle Little Star” and “Baa Baa Black Sheep”. 