my brother learned this one at camp. I guess it’s not really a handclapping rhyme, more like a campfire song. the first person sings a verse and the second person repeats it exactly.

there was a man
named Nathan Stone
he had a goat
that he called his own
one day this goat
got to feelin fine
ate three red shirts
right off the line
when Nathan saw
what the goat had done
he told that goat that his time had come
so he took him on down
to the railroad tracks
and tied him there
so he’d never come back
then the train came along
and the whistle blew
that poor old goat
knew his time was through

(sorry, i can’t remember how it ends. i know he “took 3 shrieks in mortal pain”)