If you're missing the paper entirely, it's either too small or too far away. I would try again at 10 yards with a bigger target just to get on the paper and see the groups.
The Beretta 9mms can be accurate pistols, at least by service pistol standards. Any firearm with a moving barrel that's only supported at one end will have a hard time matching the accuracy of a fixed-barrel .22 pistol.
Some suggestions:
1) Try different ammo. Fiocchi and Geco work well for me.
2) Blacken the sights.
3) Replace the Beretta's mainspring with the mainspring from a 1911-style pistol. This is a cheap and simple way to improve the trigger pull. If you ever anticipate the need to fire hard-primered ammo under adverse conditions, switch back.
BTW, I talked with someone who shot over 230 (out of 300 possible) points with a stock Beretta in a CMP "leg" match. That isn't a winning score, but it's better than many people do with accurized 1911-style pistols.