I just removed the rear bumper on my 1999 C70 to install a trailer hitch and I figured this may help some others.

DO NOT remove plastic rivets on bottom of bumper.

1. Remove all of trunk lining
2. Remove 3 bolts attaching bumper to inner fender liner on each side.
3. Remove tail lights and body filler section below tail lights.
4. On the passinger side (USA) below the light there is a blue device held in place with one bolt. This need to be removed so you can disconnect a wire connected to it that goes through the bodd and to the bumper.
5. Remove tail pipe tip.
6. Remove 2 large bolts (one on each side) on bottom of bumper.
7. Slide bumper off car.

Thanks Owenmpk

This was hugely helpful. I too have a 1999 Volvo c70 convertible and was installing a draw-tite trailer hitch. I almost removed the bottom buttons before I checked online.

A couple of other things. It took me 3 hours start to finish to get this done (not 20 mins like the instructions included say)

You need a star driver for the three bolts on each side
I was able to get away with not removing the drivers side tail light. It's much harder to remove that because of the stereo and other equipment on that side. I could get it part way out by removing the passengers side tail light only.