As PT says a photo would be useful.
Avon typically have two seat types - a plank (originally plywood but now plastic) fitting in to mounts on the tubes, and an inflatable thwart with toggles that attach to loops on the floor.
As far as the inflatable thwart goes, genuine Avon ones turn up occasionally on ebay so worth keeping an eye out - this one went for £36 last year:
Avon Dinghy Seat Thwart Inflatable | eBay
There is an alternative here:
Inflatable seat - IBS Boat Supplies
but you would need to check the length. It will have a different valve to the boat tubes which (speaking from experience) is a bit of a pain, and won't have the correct attachment points.
They are also still used on Avon river boats:
Avon Military and Profesional - AVON RIVER RUNNERS
but getting hold of them may be difficult (and expensive).
I bought mine from what was to be Aladdin's Cave chandlery in Swanwick. They used to keep a range of inflatable spares out the back - they are now part of Force 4, so not sure if they still do:
Swanwick Southampton Chandlery - Force 4 Chandlery