Adding CPVC tee to existing 1" CPVC water main line
The solution to fitting a Tee fitting into an existing straight line pipe is to also add a Union fitting. The Union is a threaded coupler fitting that comes in three parts. Two of the parts get bonded to the CPVC pipe and the third part couples them together. 



Picture source from PVC PIPE SUPPLIES

If you plan the re-assembly of the parts of the piping system carefully the final fit of the Union will just fit inline without concern of how to get it installed. Do note that you will have to have at least one side of the existing inline pipe freed up enough so that you can flex it to one side just enough to get the two glue joint sides of the Union in place. 

Do not forget to slide the threader piece over the correct end of the existing piping before gluing the union parts in place.