Noises normally come from moving parts. Around the paper tray the only moving parts would be the pickup and transfer rollers. The tray itself is not likely the source of the creak unless it happens to have some kind of a spring loaded paper tray. That being said a squeek or creak from rollers should be consistent through the entire print job, not just the end.
The best test would be swapping out the tray with a spare if you happen to have access to any. Otherwise you might wan to examine your rollers and attempt to clean them with a electronics cleaning solution to make sure there is no unecessary friction or residue.