One I remember from my childhood in Belfast in the 50s was:
Pancake Tuesday is a holiday.
If we don't get off, we'll all run away.
Where shall we run?
Down the wee lane.
Who should we meet, but the teacher with the cane.
What shall we do?
We'll chop her up in two & leave her at the hospital at half past two! (? not totally clear in the memory department on the last half of the last line!)

One of the skipping songs - one person either end of rope turning it while others jump in & jump rope - I remember:
I had a little motor car, P46.
I drove it round the corner..........And slammed on the brakes!
(At "round the corner", the skipper jumped out of the rope, around the person turning rope & back in on the other side. At, "slammed on the brake", the skipper had to jump & land, catching the rope under foot.

I'm sure many more will come to me. There always seemed to be a song for everything in Belfast