While Molokai has a plethora of condominium and beach house accommodations available, the rental rates are $100/night and up. There aren’t many lodging choices in the “budget” category.
One good choice is Hale Malu guesthouse http://halemalu-molokai.com in the uplands near the Kalaupapa lookout and the mule ride. It has 2 bedrooms in the main house available at about $50/night and a 2 room cottage which is accessible through the main house at about $80.