A sleeper is just a floor joist that sits directly on the existing floor. (i.e. it isn't "hung" from anything, it's just built right on top.)
Sounds like you need to lay 2x4s on the sunroom floor, plus 1/2 inch plywood, to raise the floor 4 inches.
Does the sun room have a cement slab floor or a wood frame floor? If it's cement, you can glue the sleepers onto the floor. (liquid nails.) If it's wood, lay the sleepers perpendicular to the existing floor joists for greatest stability and least flex.
- hope that helps. Post again with followup questions.