Ruby, there is really no traditional drum for Mr. Punch. But if you want the type with strings then this is a period military bass or side drum and will probably cost hundreds of pounds. Drums are pretty expensive instruments anyway. But a tabor would be just as traditional.
Have a look at
http://www.drumshop.co.uk/category.php?id=4
A source for cheaper equipment might be boy scouts' supplies.
Or even children's drums. Look at:
http://shopping.msn.com/results/shp/?bCatId=6475,av=12-5620685
Scroll down to
Children's Drum $31-95
It is cheap enough but well made and very usable and could be used as a tabor.
It is a snare drum, not a boom boom - but would be in keeping for a period presentation.
I don't think folk music is what you want. Certainly not if you want people to sing along - and certainly not morris dancing music.
Community song books are certainly your best bet, and they have words, and music, and often tonic solfa (doh rey me fa etc) and chord symbols. And they will include popular Punch tunes like "I do like to be beside the seaside" and "For he's a jolly good fellow".
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