I use a short 1.5 inch diameter piece of pipe inside of the 2 inch pipe at the mouth piece end of the didj. The idea here is to get the inside diameter of the two inch pipe to be the same as the outside diameter of the 1.5 inch pipe by removing some of the two inch pipe. This way you will eventually be able to cement the 1.5 inch diameter pipe to the inside of the two inch pipe with good contact.
Shown here the 1.5 inch pipe is ABS and the main 2 inch pipe is PVC. I have had no problems with any combinations of the the two types, or with using the same types. I just use whatever I have laying around at the time. The 1.5 inch pipe shown is a little longer than what I normally use. I tend to use a piece around 1.5 to 2 inches long.
The first thing you want to do here is determine the outside circumference of the 1.5 inch pipe. My first attempts at trying to bend a tape measure tape around it was too difficult to do a decent job. So the easiest way I have found is to wrap a piece of masking tape around the circumference as shown here. (Do not use electrical tape, it stretches, and shrinks. Trust me. I Know.) Overlap the ends of the tape by a half inch or more.
Now, somewhere within that intersection of the two ends of tape use a knife of some type and cut through the tape perpendicular to the edges of the tape.
Remove the tape from the pipe. This piece of tape represents the outside diameter of the 1.5 inch pipe. You are now ready for Step 2.