Super glue. Tape your rivets in place and then superglue your nutplate in place. This will allow you to rivet the nutplate without running into edges, clecos, or other items used to hold the nutplate in place.
Start off by putting the holes in your part. The best way to do this is a nutplate jig. Drilling through the nutplate itself really is not a good idea, but can be done if you are desperate. Once your holes are in place, place your rivets in the holes and tape over the heads with masking tape.
Add a couple of drops of superglue to the face of your nutplate that will touch the surface that it is going to be installed on. Install your nutplate over the rivet shanks and give it a few minutes to cure.
Squeeze or buck your rivets and you are done. If the nutplate needs to be removed it can gently be removed by tapping on it perpendicular to your fasteners. The super glue has very little shear strength.