Hmmm. Tricky one. What do you mean by economical? As that can be a matter of opinion. Invariable options will be pretty slim, economical convertible for 5k with room in the back, convertibles still hold price well, even coupe versions of much cheaper saloon cars charge you extra for having less doors. The requirement of rear seats pretty much rules out the usual suspects in this price bracket (206cc, 307cc, MX-5, Tigra etc)

BMW 3 series, around 10 years old, you wont get a diesel for that price but perhaps a 325 in good condition. An older Mercedes Benz CLK, plenty of room in that, again looking at about 10 years old and will be looking at petrol models with the vast majority automatic.

Im struggling to be honest. If you've found a good 9-3 convertible TDi model for that price then take it.

If the Golf, Focus, 306, Megane and Astra are too small, then it looks like A4, 3-series, Mercedes CLK or Saab: at that age Saabs were good cars before General Motors did their worst.

Go for a petrol: used diesels are too liable to expensive engine failures.

Thought of a volvo C70? They look good to me and will last years, no use buying a car because it does lots of mpg if it costs lots to repair and you have to change it in a couple of years. I run a 10 year old CLK convertible which I have had for three years, it's thankfully just passed the MOT and been serviced and I intend to keep it for a long time.