Yes you can lay on your stomach in the tanning bed but you should also lay on your back during the tanning bed session to get a complete all over tan.
Laying on your stomach in the tanning bed for too long can be uncomfortable so you want to alternate between laying on your stomach and laying on your back in the tanning bed.
By alternating your laying positions from your stomach to your back in the tanning bed you get a better overall tan.
However it's okay to just lay on your back when tanning but when I use a tanning bed I always tan on both my back and stomach to get the best overall tan.
If you just lay on your back you get less of a tan so it's best to go from stomach to back when using a tanning bed.