If you know some one with a rubber lined pond, they may have some left overs. Pond lining can be cut to size with scissors. It can be purchased by the foot in pond supply stores. It comes in 4 ft thru 12 ft widths. Nice and flexable and lays flat. A 1 foot by 12 foot piece will make covers for a lot of nestbox hinge lines.
I last used a 2 1/2 foot long 4 inch wide piece over a 24 inch wide double nest box lid, I used a 2 inch by 30 inch scrap of T1-11 and screwed it to the coop wall just above the hinge line squeezing the top 1 inch of the rubber between the coop wall and the afore mentioned scrap, leaving the remaining 3 or so inches of rubber laying over the top of the nest box lid and hinges.