It is usually only possible to flat tow (with all 4 wheels on the road) a manual transmission vehicle. Automatic transmission vehicles normally cannot be towed for any significant distance without raising the drive wheels off the ground on a tow dolly. So front wheel drive automatic transmission vehicles would have to be towed with the front wheels on a dolly; and rear wheel drive automatic transmission vehicles would need to be towed backwards; with the rear wheels on a dolly. If you bought a 4 wheeled flatbed car hauling trailer with electric brakes (which usually weigh about 1500 pounds and cost about $1,500 from manufacturer direct outlets), you could safely tow a vehicle with any type of transmission. Convertibles have a lower center of gravity than a sedan; so they are slightly more stable to tow. But manual transmission convertibles are rare these days; unless you get a sports car. Convertibles are also slightly heavier than a comparable sedan; although not excessively so.
Some newer vehicles may be difficult to attach a tow hitch to. This is something you'd need to check with the dealership or with a trailer hitch supplier BEFORE buying the vehicle (but here again; a car hauling trailer would eliminate concerns about tow hitches and vehicle towing compatibility). There are also some vehicles which cannot be towed because they have hydraulic pumps which run off the drive wheels; so if you plan to flat tow, you'd also need to consult with the dealer or the brand's customer service office about the towability of the specific model you're considering.
Mercedes certainly makes some relatively lightweight models, and also has some manual transmission models; but you'd need to sort out the specifics as mentioned above.
Some of the vehicles I'd suggest considering are the Mercedes SLK 300 convertible; the Mazda MX-5 convertible with power hard top, the BMW Z4 sDrive30i convertible, the Infiniti G37 Sport convertible, and the Lexus SC430 convertible. A link to an Edmunds comparison of these 5 cars is posted below.