An aerial needs to be clear of the metal frame of the car. That means that it either needs to be completely external or it needs to be attached to the windscreen.
An external aerial either means drilling holes or using a magnetic mount. The former option you've ruled out. The latter is difficult to achieve since most magnetic mount aerials are designed for CB, amateur band or taxi use, rather than for 'normal' radio reception.
That leaves a windscreen aerial. A suitable amplified aerial can be purchased fairly cheaply, They're reasonably discrete and easy to fit:
http://www.rockshore.uk.com/windscreen-car-rad io-aerial--antenna-483-p.asp
Chris