Are you in the UK?

Yes North Lancashire

The cheapest way to do this is using a system called a "split system" . This is an external condensor unit and an internal fancoil. For performace versus cost I would look at the Japanese manufacturers such as Toshiba.

To install this the supplier will mount the condensor on the external wall and drill holes to connect the pipework to the internal fan coil. The challenge will be to make sure that there are no exposed pipes and that the external condensor is out of the line of sight to visitors, etc.

Assuming that you have a loft you could also locate your fancoils above the ceiling and thence use ductwork fitted to a ceiling grille from which the air will be pumped into your room. Alternative locations for the fancoil for this option include above the bathroom ceiling

You can also look at the cost of a single external condensor which will serve the two internal fancoils within better quality internal fan coils.

Points to remember are that the fan coil units need to be serviced and filters changed therefore accessibility is important. In addition remember that these units will be audible and sometimes this can be very irritating, especially in a bedroom. As such you want a unit that will pump out a lot of chilled air at its lowest setting which means an upgraded unit. This applies even if you are using a duct and grille and the fan coil is not located in your bedroom.

I am sure that you will easily find a supplier in your area on Google as these systems are standard in the commerial world.

Best of luck and I hope that this helped.

Thanks we've decided to go with the split system using fijitsu units ducted to one external unit, work starts next week. We're using a local supplier.