How old are the kids? Young ones (3-7) love Jump Jim Joe:
Jump, Jump, jump Jim Joe
Shake your head and nod your head and tap your toe
Around, around, around you go,
And choose another partner and you Jump Jim Joe!

Olders (up to about 11) enjoy Zodiac (aka Sodio, Spodio, or Billy Billy)(Longways set with partners)

Let's go zodiac, zodiac, zodiacpartners swing joined hands to the music
Let's go zodiac all night long.

Step back, Sally, make a little alley,
Step back Sally all night long.

Here comes zodiac, zodiac, zodiacOne of the top couple goes down the alley doing something show-offy (etc.)

Here comes another one, just like the other one,
Here comes another one, all night long.