Oddly enough there are two ways to get "stinky stuff" in the typical cheap marine head. It flushes with seawater, and if there is seawater left in the lines or in the bowl, that gets really ripe after a couple of days of stagnating.
Or--the joker valve (looks like a big duck bill, supposed to close by itself to keep the sewage "out" downstream) eventually fails and lets sewage back into your bowl. Just as pleasant.
Either way...Sounds like time to knuckle down and either replace the whole thing (I'm another Lavac fan, they're just a better way to go, if I may make the pun) or buy an overhaul kit, which used to be about 1/2 the price of a new cheap head.
Plenty of web sites to explain head plumbing options. Bottom line is that for a stinkless bowl, either you flush with fresh water and then pump it dry, or you pump it dry and keep it dry, which means everything has to be working right. Rubber gloves, chlorox, roll of paper towels, some plastic trash bags and a helper, and it is no fun job but no big deal to overhaul or replace.