20x2.25 is pretty big for moped wheels, that's more into cycle territory, BUT...I think I can venture some assitance.
Cheng Shin, and their american counterpart Maxxis tire&rubber company, make some very very nice tires in a multitude of sizes, and since they make them in moped sizes as well, it's very likely that you can find what you need in thier stock, I shall have a look myself, and maybe post the results.
As for tubes, believe it or not, I've gotten excellent performance out of BELL self-sealing bicycle tubes by buying them 1-2 inches oversize, but I am not so sure they'd fill out a 2.25 tire...I've only gone up to 2.125 on those, still, it's worth a try.
-R