Can you use a tanning bed after getting nipple piercings?

Yes, but be very careful because tanning can dry out a piercing.

A sunburn would put stress on your skin & slow the healing of your piercing. Your skin will be distracted from healing your piercing because it is trying to recover from the sunburn as quickly as possible. A sunburn on the actual piercing itself would cause even more trauma to an already injured area.

If you simply cannot live without tanning, cover the area around the piercing. You'll also need to be absolutely sure that you won't end up burned after your session, so you may want to reduce your stay in the bed just to be safe.