The cruise ships generally arrive on Tuesday, Wednesday and Thursday and dump 2000-3000 people on the area, so any day but those are okay. We went on a Sunday and the start of the tour at the beach was crowded with locals on family picnics having fun. The tour guides lead you on a tight schedule so each group mihg tseem crowded.
The advice most often given is to visit Dunn's River Falls on a day when cruise ships are not in port. Here is a schedule for the port at Ocho Rios. Just select the month you are traveling and see when the ships come in.
The best day to visit Dunn's River falls is whenever there are no cruise ships in port which usually on sundays. Also on sundays the crafts village is not open the crafts people are attending church. Now isn't that special! Try to avoid the craft village you won't be sorry
Somewhere there is a schedule showing when all the cruise ships are there. Pick any date there are none and it should be good. I would think the middle of the week would be good but anytime there isn't a cruise should be good.