Hi AzureStarline - we don't have a convertible, but we use a little harness clip thing we got from a petshop locally to secure our pup in the back of the car - it's about 18" long and has 3 types of seatbelt connector on one end (so that it fits all types of cars) and a standard trigger clip like on the end of a lead - we clip this to her collar or lead - it can be shortened/lengthened a bit and was about £3.50 - so we have one in each car permanently plugged into the middle seat belt in the back.
I suppose depends how much your dog moves about in the car generally - we find that Ruby likes to put her head on the armrest, so she's sort of in the front with us (bum on back seat, front legs on floor)
The seatbelt through the harness thing that Dylansmum suggests would also work too