The phrase "a nap on" is correct and usable in written English.
It can be used when referring to taking a short sleep on a specific surface or location.
Example: "After lunch, I decided to take a nap on the couch to recharge for the afternoon."
Alternatives: "a nap in" or "a nap at".
Having a nap on one of these reclining chairs is a must during a stay in Paris.
We really took a nap on this one.
In one scene, Jim takes a nap on the couch.
At sundown one day, I woke from a nap on the couch, and made my way to the table where I kept my volumes of collected poems.
A popular custom is to take a nap on Shabbat afternoon, in part to avoid transgressing one of the prohibitions.
Sometimes I'd take a nap on an exam table while she caught up on charting.
Then we go home and everybody takes a nap on the bed.
When she was completely wrung out, she'd take a nap on the floor by the typewriter.
Suggest that she take a nap on sheets that you also cleaned.
He extends his prayers to half an hour while Leila takes a nap on her couch.
As the play opens, a stoutish man is discovered making plans to take a nap on the beach.
