I would take it to a car stereo shop. If you’ve just blown out a tweeter cone, they’ll replace the speaker (though they’ll most likely want to replace speakers in pairs).
BTW, don’t leap to the conclusion that you can’t do it yourself. The hardest part of replacing a car speaker is usually getting the inside door panel off, which, I grant you, is no picnic. But isn’t actually hard: it’s just tedious.
What year is the car? Is it still under warranty? If the answer to that last question is yes then the dealer for sure.
If the car is no longer covered then the issue is a bit more complex. The stereo shop might be cheaper, their speaker might not fit very well, and the connectors may be different both of which will require modifications. Some shops can do this work well others are hacks and will fuck it up.
Rick’s advice and cautions are on target. Although KneadToKnow is correct that actually replacing the speaker shouldn’t be hard, removing interior panels can either be very easy or ludicrously difficult, depending on the manufacturer and the designer team’s attitude to ease of maintenance. I assume this is a (BMW) MINI Cooper (not the original design Mini), and so the interior door panel is probably held into place with a combination of concealed screws and plastic clips, and will probably take just enough brute force but not too much to remove (try quantifying that in a Haynes manual). You definitely don’t want to break plastic bigs, as this will likely end up in you having to procuring a new panel or jury-rig some fix to keep it from vibrating around.
If the speakers are brand name (i.e. Bose, Harman Kardon, or somesuch) then they’re probably a standard model and you can just buy them off the shelf, and they’ll fit in standard mounting. If they are some generic brand, you may need to drill new holes or whatnot to mount them, which is a pain in the ass. Your best bet may to be to call around to salvage yards and see if you can find them off of another MINI; that shouldn’t run you more than US$5 or US$10 (typically).