To my knowledge Hungary only produced arms in the FEG factory in Budapest. They made Mannlicher/Steyr M95's, Mosin Naget, some Mauser's then AK's. Along with many pistols. You may find a sporterized service rifle or possibly have one done for yourself. Looks like some Mannlicher-Schoenauer may be made in Hungary. Are you Magyar?
I am. I have a Mannlicher M95 a Frommer Stop and a FEG PA63 I picked up fairly recently. I hope this gives you a little insight. Maybe someone has some more up to date knowledge.