I'm not sure if Minarelli engines are still produced, though I suspect variations on the V.1 (which is on most mopeds) are made. Minarelli still produces engines, mainly for small tractors and things.
But there are many junked up mopeds that have working engine parts. HandyBikes or other moped shops carry them. I also know a guy in Italy who can get parts and will ship to the US. He's reliable and not expensive (I got a 14.12 carburator for less than $30). He said he can get other parts and such. Email me if you want his email address and need parts.
You might also be able to use body parts form other mopeds if you need them. The Decepticons have some "chopper" models w/ different parts. Like Garelli forks on a Sachs. Things like that. I think many frame mounted tanks, for example, could go on any moped. Either way, it is TOTALLY possible to keep Minarelli-based mopeds fixed and running.