I have a few that might work for you.
Bar-B-Barn, very inexpensive inn type resort. On site dining, friendly bar and great beach.
Coral Seas Garden, the cheapest of the 3 Coral Seas properties. All inclusive is available. What's nice is you get to use the other Coral Seas properties as well. This place is known to be popular with birders.
Sea Splash Resort, Right on Negril beach. Restaurant on site along with pool and jacuzzi.
If you like the west end of Negril (cliffs area) then the next 2 properties might be for you.
Banana Shout, pretty much the quiet area of Negril. This place is close to Rick's Cafe (a very popular watering hole for tourists)
Xtabi, This property is built right on the cliffs. It has 5 caves that can be explored and great snorkling in the waters below. It also has a cliffside restaurant.
Hope these help you in your search and I hope you have a great honeymoon.
Adam aka Big Dude