Here;s a list from Lan Sluder, BelizeFirst.com
Tina's, Caye Caulker --
Blue Wave Guesthouse, Caye Caulker
Falconview, Santa Elena
Cayo Backpackers Hostel, San Ignacio
Pedro's Backpacker Inn, San Pedro
Nature's Way Guesthouse, Punta Gorda
Depending on how you define hostel, you could also include a number of other places, including
The Trek Stop in Succotz
Amigos on Turneffe atoll
Glovers Reef Resort on Glovers atoll
Two or three of the places on Tobacco Caye, including Gaviota and Tobacco Paradise
Hummingbird HideAway, near Corozal Town
Spiritwind Reef Resort, Dangriga (the dorm section)
BFREE, Bladen, Toledo
Paradise Vacation Hotel, Placencia village