Well, one that I've always thought was rather strange - not necessarily advocating you teach this one - not sure how social services would view it
Peter, Peter, Pumpkin eater
Had a wife and couldn't keep her
Had another didn't love her
Up the chimney he did shove her.
As sunnyday says, hard to answer without knowing which you already sing.
Action and number rhymes are always good;
Here are grandma's glasses
Dingle dangle scarecrow
London Bridge is falling down
Oranges and Lemons
5 little ducks went swimming one day
5 cheeky monkeys swingng in a tree
5 naughty monkeys jumping on the bed
10 little aliens