How to Secure a ceiling register tight?
If I understand the problem correctly , you may be able to get a piece of metal (like a scrap piece of duct or just buy a small piece) fold it so it is not wider than the register on the register side and 2" or longer on the inside the width of the opening is best but a 1" wide strip can work. Use a 3/8 self piercing (not self tapping) screw to hold this piece in place, do this on each end. If the fit is not tight enough I have stuffed some fiberglass insulation behind the metal until it will almost hold without screws, then add your screws they will bite the fresh metal and pull on the old duct providing a better anchor point. I have done this especially when the hole in the duct has stripped out. (I do open the original hole so it will all the torque on the new metal). I mention to hold the new piece with self piercing because self tapers cut two much metal and don't hold as well. The self piercing are just a very sharp tapered screw this works best with duct work. 3/8 so you don't punch through the 2 layers of metal and sheetrock. Hope this helps I have used this trick many times on remodeling jobs it really is quick and cheap.