I don't believe for a second that all accomodation is booked up in Magaluf. My friend actually just booked a week holiday at the Fiesta Jugle and you don't get more central and party than that hotel.

DaveyK, I am not sure if you used to booking holidays DIY but go onto travel republic and find an apartment. It is really easy and you will therefore be no worse off and can use your flights.