PVC to PVC??

I just replaced a the last section of cast iron with 3" PVC pipe in my waste line. Now I need to couple the the end of the new PVC to the existing PVC. What can I use to connect the two ends? The rubber couplings I've been using have a ring in the middle, so I can't slide them up and down. I don't have any vertical play in the stack, so I can't lower the existing stack into the couplings. Any ideas?

Are you using a banded coupling or, a no-hub? You should be!
Loosen the metal band and slide it out of the way. I usually tighten it a little bit just above the rubber so it stays there, Take the rubber and roll it back over itself half way then slip the pipe in place and roll the rubber back down over the pipe. Put the band in place and torque it up!

Or you could use a repair coupling. It's a regular plastic coupling without the stop in the middle. Clean the inside of the coupling first, then slip it over one of the pieces of pipe and slide it out of the way. Then clean both ends of the two pipes. Before you apply the glue to the pipes, put a mark on each piece so you know where to slide the coupling. Then apply glue to both ends of the pipe and slide the coupling into place giving it a 1/4 turn when there.

I rarely use repair couplings... I believe there is a higher ratio of success with using a no-hub.

I have used those double ended couplers in that situation. Each end has a compression fitting that slides over the pipe. I pulled the upper pipe over, slid the whole coupler over the one pipe, realigned it over the lower, slid the coupler down till both pieces had a fiitting over them, tightened each end and was done....