Last year I had a 4*8 outdoor plywood board (pressure treated I think)
cut into appropriate pieces at the local Home Despot and put together
a little house for a few feral cats. I used some polyurethane stain,
caulked the seams, and figured it was pretty waterproof. Yet every
heavy rain the inside was soaked.

I figured that I'd get some of that roofing tarpaper, use the flashing
cement to attach it to the wood, and put some shingles on it. However
I can only buy the tarpaper in large rolls, which is far more than I
would ever need.

So, what's a good way to waterproof a pet house?