Hi Sooze,
Sorry personally I cannot help you with actual tour operators that do self catering apartments in Sliema, however I can suggest a few if you fancy booking direct. These three are all situated main Sliema front, very regular buses to all parts of the island, just across the road from the cruises and Valletta ferry boat.
My relatives have stayed at these so I have actually seen inside the apartments.
http://www.115aparthotel.com/pages/hotelselfcatering.htm (Next door to the Kennedy Nova Hotel)

http://www.mol.net.mt/giorgio/

I haven't seen inside the apartments, but last month I spoke to a couple who have been visiting the island several times a year for the past 27 years and have often stayed here.
http://www.mol.net.mt/pebbles/

I've been reading through your postings to get a little idea about your ages and tastes, you might also consider Mellieha. Beautiful scenery and beach, a good range of various budget restaurants, not a clubbing area but some excellent bars offering a reasonable priced pint and live music - never noticed any Burberry The Luna has had some good reviews on this site, you could ask other members for the name of the operator they booked with.
http://www.lunaholidaycomplexmalta.com/home.htm

Another nice place for self catering is Pergola

http://www.pergolahotel.com.mt/about.htm

Both Sliema or Mellieha would be ideal for you - hope I have been of some help.

I don't think there are all that many s/c apartments in Malta (compared to spain etc!).

We stayed at the Crowne Plaza in Sliema, and it was ok - not the 5* it was supposed to be, but more like decent 4*, once they moved us to a room without dampness!

Breakfast was great, and I'm sure we must have had a fridge in our room, as I remember buying cokes from the supermarket which was large, cheap and not far away.

Only thing that was lacking was night life. Bars in the area closed fairly early at night. We went into St Julians a few night, but it was pricey for a taxi back (£10).