I've put together different things with PVC and I never use clue. As someone else said, you can use a lot of different types of connectors. If I needed extra reinforcement I drilled a small hole through and put a stainless steel screw through it, then twisted over the ends. I only did this on the bottom in hidden areas.
Be careful when cutting or drilling PVC pipe as it releases toxins into the air. Should be done outside or in the garage away from the main living area of your birds. I use foam beads on my toys and they should be latex free. If building a play gym, you can use vet wrap to wrap the "perches" (will need to be replaced frequently) so the bird doesn't slide around. My Macaw has a home made play gym made of PVC pipe but I stopped using the vet wrap. He's fine with it but also has a Get-A-Grip attached to the playgym and ceiling for perching/playing.
Like others have said, my pvc play stand didn't need any glue. The connectors are designed to make a really snug fit if you push the tubing in nice a tight. To separate the tubing from the connectors when I want to make a change to the stand takes all of my brute strength.