Are you reading in all 9 bits?
I haven't used that part, but the datasheet is pretty explicit on extending resolution, although it will require some additional programming on your part.
If your temperature doesn't change rapidly, you can pick up more stability by taking a moving average, where you take the most recent N samples (N=an integer of your choice), sum them, and divide by N. If you make N=2^n, then division is simply dropping the n least significant bits.
Also have you done a Google search for "DS1620 PIC"? You might find some tips this way.