Good advice from Will above,
the second quarter of the year is ideal.
More importantly... what of the types of critters that you will likely see? Remember- this is
Nursery Time in the western Caribbean. Nurseries are found in the calm protected and shallow reefs that are bathed in Sun light.
As much as Will loves his "North Side", remember that the real treasures of Roatan are the denizens of the South Side. Nowhere else in the Mar Caribe can you find this concentration.
Do some

here, but understand that the geographical barrier presented by the island causes the South side to be shallow, lush and full of creatures in the nursery stage... especially at that time of year.
Diving on the South side is "very advanced". No- not in terms of technical diving or currents... To get any enjoyment out of it you must have great buoyancy skills and excellent observational abilities. Follow your DM closely, take a flashlight and
be very amazed. Seahorses and their elusive cousins, the Pipefish are seen on almost every dive.
I see by your profile that you also hunt. Your keen eye will be of benefit.
The North side (aka West) is a delight as well, but it is more geared towards the common larger creatures that used to be endemic to the Caribbean. With the N/W side's enhanced environment, due to the Marine Park's efforts, any diver can spot a Lobster, a Grouper, and so on. It is also co-located with on-shore
party central, the West End.
I don't work for a South side (or any) operation, I don't even live on Roatan any longer. But when I return, well... I've already seen a hundred Groupers. I go for the rare stuff.