It should be possible - but would take a hell of a lot of cash to get it done, as I don't think you can get a kit commercially. It is also a very involved process - you can't just cut the roof off!
I've got a picture somewhere comparing the Cooper S convertible and its solid roof cousin in terms of chassis structure. The convertible needed extra metal in the sills, in the floor, bulkhead, some in the engine bay, and a few other bits. You would also need a roll over hoop behind the B Pillar, and the hood would need to be custom built.
Mind you, could always have a Punto convertible - there's a N plate Punto cab. for sale round my way for 1900 quid IIRC. I thought it was a bit pricey, but I would guess converting a Cinq would cost a lot more, especially if you can't do the bulk of the work yourself!