Can anyone recommend a good maintenance-free rear shock?
All shocks require a little bit of love from time to time. A coil rear shock will require less maintenance than an air shock. The simpler the shock, the less maintenance you will need to do. I have only ridden fox in the back, but have never had any issues. I would recommend looking at the Fox Van R Coil. The Rock Shox Vivid would also work really well.

If you want to be able to pedal well, you should look at the higher end coils that have propedal, or airshocks.