"I Had A Dog And His Name Was Blue" is a personal favorite of mine. Kids (all right, my friends and I) seem to enjoy really stretching out the "Heeeeeeeeeeeeeeeeeeeeeeere, Ole Blue" part.
Have you tried a simple blues riff that kids can make up lyrics to? That can keep both grownups and kids happily occupied for hours. Last summer, I spent an evening with about eight adults and four kids making up lyrics about the evening, each other, and the kids' large dog, who was named Buck. My contribution was: (to the tune of (I had me a cat...the cat says fiddle-i-fee.)
I had me a dog, and his name was Buck
Wish I could think of something
That rhymed with Buck....
Years ago, one of my girlfriends had a boyfriend named Bud, whom we called Buddha. Buddha owned a small landscaping company, and we spent many happy hours extolling his praises to the tune that drill sergeants sing when marching their recruits around the base. (I'm sure the tune has a name, but I can't think of it.)
Buddha's gang works real hard
They put the voodoo on your yard.
Buddha's got a pickup truck
Your friends will say your yard don't suck.
Buddha there and Buddha here
Buddha wanna have a beer
(Nobody ever said these verses had to make sense.)