I was going to suggest any Beatles tune that Ringo sings, as his bandmates were careful to write for his extremely limited vocal range.
“Smoke on the Water”?
ducks and flees
Heh… that was the first tune I ever learned to play when I was a kid, and yes it was on a one octave xylophone w/o sharps or flats.
Here it is in regular CDE format and my attempt at the OP’s strange format 
:
Doe, a deer, a female deer
C D E C E C E
A B C A C A C
Ray, a drop of golden sun
D E F F E D F
B C D D C B D
Me, a name I call myself
E F G E G E G
C D E C E C E
Far, a long long way to run
F G A A G F A
D E F F E D F
Sew, a needle pulling thread
G C D E F G A
E A B C D E F
La, a note to follow so
A D E F G A B
F B C D E F G
Tea, a drink with jam and bread
B E F G A B C*
G C D E F G H
That’ll bring us back to do-o-o-o-o-oh.
C B A F B G C G F E D C**
H G F D G E H E D C B A
Note: C* indicates high C, the highest note on the instrument.
It’s been a while though so my memory could be a little bit rusty.
You can play the Futurama opening song on a toy xylphone. Unfortunately, I don’t have access to one now, so I can’t give the notes. But it’s definately possible.
Um…no. That’s not right.
in the key of C, it’d be: C-C-C-F-F-G-G-G-F-F At least, for the beginning.
My brother’s girlfriend’s five-year-old has a toy guitar that has six or seven surprisingly realistic “chords” played by pressing buttons on the fretboard. My dad the guitar fanatic plays “Smoke on the Water” on it, to the kidlet’s endless delight.
I have an odd family.
Do ducks have fleas? 
They mite.
I probably should have stated how LONG the robot played it. I think it only played the first two lines. It was still head and shoulders above any of the other groups.
I’ll link to a video of it here when I update the class website. (Unfortunately, no sound)
That really bugs me.
(Dody Goodman once wrote a book mentioning a group called The Armpits, who had a hit with a song “Don’t-a-Bug-a-Me Baby.” )
Here is a link to the webpage with pictures and movies of the robots playing the xylophone. I think you will agree that none of them do it particularly well, which is why I will probably give it again as a project this semester.
Musical Robots
The first movie is of the group that played “Take Me Out To The Ballgame”, but on one of their poorer runs. Their timing relied a bit too much on the arm being started in exactly the right position.
(The minimum criteria was to play four notes on two keys with some semblance of rhythm and capable of playing a different song from software changes alone.)
[QUOTE=The Asbestos Mangoducks and flees[/QUOTE]
Ducks and fleas and geese better scurry
When I take you out in a surrey…
As befitting a resurrected zombie?
The theme from Tubular Bells (aka the theme from The Exorcist):
E-A-E-B-E-G-A E-C-E-D-E-B-C
The First Nowell - one octave C - c, no accidentals.
I can get pretty close to “Yankee Doodle” on one of my son’s xylophone toys, but most of them have the wrong set of notes for it to sound right.
At least the first part of the Star Wars theme.
1…5…4328…5…4328…5…4342…
Sorry it makes me too crazy to write it with 1=A, 2=B… because notes already have letter names, and those aren’t them. (Actual A-B-C-D-E-F-G-highA would give you a minor scale.) I know, I’m way too OCD/pedantic…
The [Zombie] Lion Sleeps Tonight
You can actually make a decent version of it on a 5-note toy piano, if you can play two notes at a time:
[I agree that the OP’s A to H scheme is better replaced by a 1 to 8 scheme, so I’m using that]
1+5 (repeat three times), 1+4 (repeat two times), 2+5 (etc.)
Brahms’s Lullaby
Finlandia (main theme) by Sibelius
When The Saints Come Marching In
Oh Susanna
Row Row Row Your Boat
Two Beatles songs: Nowhere Man and All My Loving
A La Claire Fontaine (French folk song)
I’ll post more later if I can think of any more. 
Some more:
Theme from ‘‘Spring’’ by Vivaldi
On Top of Old Smokey
This Old Man
3 Blind Mice
Twinkle Little Star
Old McDonald
London Bridge
The First Noel
Big Rock Candy Mountain
Maybe also Blowing In The Wind.