There is no reason why you shouldn’t be able to tow a caravan or trailer with a convertible, however, as with any tow car it will need to be officially approved for towing by the manufacturer. This can usually be confirmed on the manufacturer’s website.
Another rule to follow is that the total weight of the caravan should not exceed 85% of the tow car’s kerb weight. This applies to any vehicle, regardless of whether it has a convertible roof or not.