First of all get a mirror or hold scope bell up to bathroom mirror under very bright light. Have scope adjusted to setting you shoot with. Now look in scope while bell end is completely flat against mirror. You should see the crosshairs reflection. Adjust until it matches crosshairs in scope.
Definitely get FX no limit, Burris Signature Z, BKL, or any other fully adjustable rings. Zero the rifle as close as you can by adjusting the rings, then use your turrets to fine tune.
Before you do any of this, you might want to switch out scope & rings to see if any other combo works. I like to center all my scopes but some spring guns don’t do well with adjustable rings.
This problem is one reason I prefer open sights on any gun as an option. With see through rings if scope doesn’t match the open sights you know right away scope or barrel band has been bumped or scope is defective.