It may be possible to replace the tank bladder, but that job is not easy, and the replacement bladder will probably not last nearly as long as the original did. If the problem has been going on for some time, I would expect the inside of the metal tank to be rusty and rough--not easy on a new bladder.
When I had a similar problem, I tried to replace the bladder in my old tank, but when I got in there, I found a real mess, including places where the bladder had bonded to the inside of the metal tank. I took the replacement bladder, which was a very expensive part, back and got my money back.
I ended up buying a new captive air tank that was recommended by a friend who had a pump service business. It cost about 4 times what the replacement bladder cost, but also is a much larger tank. That tank has worked fine for about 10 years (hope that doesn"t jinx it!!!) and it was a whole lot easier than fighting that new bladder into the old, rusty tank. And maybe needing to do something to it a couple years down the road.
If I was doing it, I would just bite the bullet and buy a new tank. I would also buy the largest tank that is practical, since that allows the pump to cycle less than it would need to with a little tank. Hope this helps. Good luck!