It's going to depend on the number of drops, how easy it is to run duct work (a large attic will be favorable), electrical (do your existing panels have the capacity to add central? 

There is no traditional "duct" work going thru the wall.

Duct work also stolen from home.

The A/C UOP is made up of ductwork and the A/C unit and it's parts.

I live in St Louis, so the desire for central air means ductwork is really an expectation.

If your units are small enough to get by on a window unit for cooling, you may be able to avoid installing additional ductwork to deliver heat and air conditioning.

If there is existing duct work and copper but the system is missing or has been stolen then I think you could get a new one installed for closer to $3500.

It can be found at https://dl.dropboxusercontent.com/u/105466347/713bonniebrae.pdfPLUMBING: Replace PVC piping connections to water heater with copper (37), repair or replace damaged ice maker (45); replace damaged dishwasher hose (48), replace leaking pipes under sink (49); replace sub floor under tub and toilet with accompanying tiling to area floor and address relevant leak(54); replace flexible drainline(64); Install missing bathtub drain stopper (62); add backflow prevention to outside spigot (91)STRUCTURE: Replace hurricane straps with approved nails (71); reclean ductwork (74); extend gas fired flue (86); Remove standing water; dig vent wells and/or repair basement walling etc to stop water entering crawl space (87); insulate water pipes in crawl space (92)ROOF & GUTTERS: Replace damaged duct end-cap and cover (10); Add downspout extensions to divert rainwater away from house: Add matching gutter extensions to extend from roof into gutters; Clear moss from roof (20); Add splash blocks and diverter pipes away from structure (14); Replace rain boots and do remedial roof work(13/15); align gutters properly and renail to fascia for correct flow(16); extend downspouts into gutters (18), clean out downspouts and gutters (19); repair leak point (70)ELEC & HVAC: Install 1 carbon-monoxide detector in hallway near base of stairs (27); Install balance of internal coverplates as well as exterior outlet cover (28,29); Make good loose light fixtures (30) and attach faulty dishwasher bracket (46), replace HVAC filter (77)INTERIOR: Remove old or molded caulk and silicone to tile in bathrooms (58,59,61,63)and and kitchen back-splash (50).

I also have some minor ductwork that needs to be done.Any contractors you can recommend are appreciated.  

There is some ductwork from previous owner, but one guy told me it's not useable, and that I have to go with metal.