I don't think there will be turtles nesting in April. I have never seen them in early May.
For others who will be there in June/July, here is the info from the latest VM.
Due to last years overwhelming success, we are
again offering a special sea turtle program on
Monday evenings this June and July. The session
begins with a special presentation hosted by
a staff biologist with the Caribbean Conservation
Corporation (CCC) and is followed by a field trip
to Archie Carr National Wildlife Refuge to see
a nesting turtle. The cost for the program is $20,
which includes an adopt-a-turtle packet
with an adoption certificate, name and
photo of a loggerhead sea turtle, a sea turtle
fact sheet, and a one-year subscription to
the CCC newsletter (one per household).
Disney Vacation Club Members can make
advance reservations for both the presentation and
field trip by calling the CCC at (800) 678-7853.
Payment is due at the time of reservation.