I have a 125 amp. Bryant main panel that is maxed out with piggy back breakers. Can I feed a small amp. Panel off the main if I remove some breakers and put them into the sub panel , I need to run a 2 pole 30 amp. On the sub panel.

Yes, you can remove two breakers from the main panel, install a 50 or 60 amp to feed the sub, and move the removed circuits to the new.If you do this you will need more details.

To feed the subpanel try to get a Cutler Hammer type BR (BR260) or CL (CL260) breaker. That is the approved replacement breaker for a Bryant panel. Bryant is long gone. Ideally if you're re-using the breakers from the main panel in the sub panel, try to get a Cutler Hammer panel as well. Or just use new breakers in the subpanel