Early April - this is usually part of the Spring Break season at DLR. That tends to mean longer operating hours with more evening entertainment, but high(ish) crowds. DLR doesn't do much for Easter, but they do have the Egg-Stavaganza and there may be some Spring decor. If you're looking to go this year, it will be after Easter, so the Easter activities may be over by then; in 2017 it'll be before Easter.
Early October - the parks should be in full HalloweenTime-mode, which is a lot of fun. It tends to be very crowded in the parks during this time because of the Halloween overlays and offerings. The weekdays may not have long operating hours or full evening entertainment and there will probably be Mickey's Halloween Parties during the week.
Late August - this is the end of the summer season, so some things are starting to wind down. Crowds may still be high and there is usually a bump in crowds right when the AP blockouts end. Haunted Mansion will likely be closed to have the overlay installed.
Halloween is my favorite time of the year at DLR, so despite that probably being one of the busiest periods, I would probably go with the week leading up to Columbus Day.