Blue jays empty my bird feeder tray...

Try using a tube feeder instead. Many backyard bird-watchers rely on this old standby. A good tube feeder should be well built and made of clear plastic, so that you can see when you’re running low on food and the birds can find the feeder. Two big advantages of tube feeders are that they are tidy and that the small, individual perches are perfect for small songbirds but discouraging to larger birds such as blue jays.