Best way is to e-mail a few of them: Malta School of Flying, European Pilot Academy and Diamond Aviation.
You should be able to get checked out and then permitted to fly solo at any of these schools. Diamond Aviation only operates a single DA40 and so availability can be poor (unless you fancy hiring a DA42 at 400 EUR+ per hour!) and is of course a bit more expensive than your typical spam can.
I believe that European Pilot Academy have a Tecnam P2002 which is probably the cheapest on offer (around 150 EUR per hour Dual off the top of my head...) and Malta School of Flying have a C150 and C172. You'll need to e-mail them for prices as they don't advertise them online.
A few other things to consider:
ATC is ok - they speak fluent English and clearances are easy to understand. The only problem is that during peak periods (i.e. 5 arrivals per hour!) they consider themselves a bit like Heathrow and so VFR traffic is often stuck orbiting out to sea for 10 minutes at a time waiting for a chance to land. There is a cross-runway 05/23 so provided that the cross-wind isn't out of limits then using this instead of the main runway can speed things up.
Forced landing - let's hope it doesn't happen but places to put down are sparse. Agricultural fields here average around 150m long and so it's either that or the sea.
Weather - typically CAVOK from June-September. Early morning mist and sea fog can occur. Mediterranean can get quite strong winds from time to time, including in the summer months it's not uncommon to have a 15 cross-wind. Flying after 10am or before 5pm can be unbearably hot inside the aircraft whilst on the ground!
Sightseeing - Let's face it, Malta is tiny. You could lap the entire island, including Gozo, in around 1 hour. Consider flying a couple of hours Dual with an instructor rather than trying to get signed off? After you've seen all of Malta and Gozo, your next nearest land is Sicily (100 miles) and don't even get me started on the ATC over there..
I think that's all but let me know if I can be of any more help.
Source: I'm an expat and did my MEIR out here.