A great question! Edit: I repeat everything already answered before:
In-flight Entertainment on 737-800
I am almost certain that the personal AVOD systems are only available on the "long-haul" aircraft with the longer first-class seat pitch. All the rest below is based on that assumption. Look at
the Copa fleet page, and click on the "detalles tecnicos" for the 737 A and B versions. The B version image clearly shows the screens, the A version does not.
I think the only way you can tell you're getting a B version is to look for Row 11 on the seat map at booking--and hope it's absent. The
737-800 "version B" as Copa identifies it, has 16 Clase Ejecutiva and 138 Y seats, with rows jumping from 10 to 17. It has one fewer row than the A version with 144 seats.
That extra row is 11.
I don't know how to know after booking however. Maybe revisiting the "select seat" option on the manage reservation page? Copa's flight status page does not distinguish between the 738s.
Planespotters.net indicates which planes are which, if you know the tail code in advance. Flightaware.com will provide a tail code with a subscription account. Flightradar24.com doesn't seem to post the aircraft in advance. A subscription to expertflyer.com shows the seat map in advance. I tend to think that Copa fairly consistently uses the B models on longer flights, and that looking at histories or dummy bookings can give you a high level of confidence.