This is a rhyme with a long history, though for all that there is surprisingly little variation. But I found a lot of variation in the tunes used on YouTube, so checked it out on Wikipedia, where I found a tune described as “most commonly associated” with it. It works very well with the guitar as follows:
CCCC, GGGG, CGCF, FCG-G7C
tune to follow…
Pussycat, Pussycat, where have you been?
I’ve been to London to visit the Queen.
Pussycat, Pussycat, what did you there?
I frightened a little mouse under her chair.