Here's are photos from two different mfrs of a PVC vented loop with an air valve installed and a spare next to it and a drawing that illustrates where they go. The air valve in the bottom photo has an integral diaphragm...you'd replace the entire "cap."
The same happened to me during last year's cruise. I couldn't get a pump-out so in desperation, I pumped it down and stuck a coffee cup in the toilet. It worked until I got a pump out the next day. The problem? As usual, the joker valve.