Now that summer is here with a vengeance, check out this list of classic convertibles that won't break the budget. After British Leyland absorbed British Motor Corporation, development all but ceased (beyond that which was necessary to keep it legally sold in the U.S.). 2. 1985 Buick RivieraThe 1980s Buick Riviera and Cadillac Eldorado were the first officially sanctioned GM convertibles that were produced since the full-size Cadillac Eldorado went out ofproduction after the 1976 model year.