There are many places in Negril that would accept us$1000 for the month of May, but remembering nh420er's "only requirements are a swimming pool and security. Also want to be on the beach", that does make things a bit more difficult to fulfill.
That would rule out the West End (cliffs), which is always less busy than the "high rent district" of the main beach. But in keeping with nh420er's requirements, Fun Holiday and Legends both would have deals that time of year, both are on the main beach and both have pools. They run in the same price range as White Sands, which does not have a pool for all their guests. Contact both of these hotels directly and refer to this thread. Both properties should be aware of this conversation.