What's the best most cost effective way to soundproof a ceiling

Make a dropped ceiling frame out of wood using (e.g.) 2x2 lumber beams, stuff the space behind it with glass wool (called fiberglass insulation in the US) or mineral wool. Cover the wood frame with some board material, such as paper-faced gypsum boards. For bonus points, cover the boards with sound absorbing foam (not very pretty though). Also, make sure to stick foamband on the surfaces of the wooden frame that come in contact with the walls, and do not let the boards touch the walls.

1. sound goes where air goes: so make sure all openings into the walls/ceiling are airtight (outlets, air ducts etc...as soon as there's an airleak part your new ceiling construction, that ceiling was a waste of time & $. 2. MASS stops sound. fuzzy insulation dampenens it a bit, bit you want mass, and to decouple it from the current ceiling, so install resilient channels at 12" oc perpendicular to current dirction of floor/ceiling joists, then install 2 layers of 5/8" drywall- the last layer is glued to the first layer (that is screwed in place) and shored up or temporarily screwed to the first as it dries. Use a drywall glue recommended for use in acoustic wall construction. Seal all edges at the perimet walls (again- sound leaks will kill your assembly if not sealed- use an acoustical caulking material. If really serious check out netwell.com for products like dBBloc... good luck.

Install a shag rug upstairs when they aren't home.