Stef,
Their apartment is your best option by far, costwise as well as for comfort. Do they not have availability during your planned stay?
The only other viable option is turning to
www.loquo.com (the Spanish version of Craigslist) for anyone in Malaga with a flatshare to offer. You will need assistance from a Spanish speaker to get the best deals, but
here's an example of what's on offer.
Here's another one, conveniently close to AD's offices and to the train station (for your trips to the airport). PM me if interested, I'll be happy to ring them up for you.
If you will be training during the high tourist season (from now until the end of August), avoid hotels, hostels, pensions, and all the rest. Prices are high, places are noisy, quality is low, and of course you will have to eat out which although not expensive, is not as cheap and convenient as having your own kitchen.
Plan 'C', ask in the Spanish section for the name of the main Spanish pilot forums (I think pilotosdeiberia.com is one of them), and post there, perhaps locally-based crew can assist.
HTH. Best of luck with your training.