You can use them offensively without Gunships, even. Just make more of them, and plop them down next to the target city one turn in advance. You'll need Guerrilla or some such terrain defense specialists, a Medic, and a bunch of other Paras with Pinch and Combats (or Drills, if you prefer). As long as you can reduce the defense to 0 with Bombers, they do well enough. If you have enough air power to do significant collateral, they do REALLY well. Gunships have the disadvantage that they only move 4 tiles at a time, and then are extremely vulnerable to attack from SAM infantry. They're great if you can put Blitz on them, but otherwise, I don't bother.
If the majority of your ground force is in Paratroopers, they can move up to 6 tiles into enemy territory before taking a city. If they have Drill, they can do the same thing again next turn. The great thing about this is that AI cities rarely have more than 6 tiles between them anyways. If the AI is seriously lacking in air power compared to you, it's not even a contest. Just hop your Paras from city to city, taking one city every other turn using a stack of Paras. If you need more bombers and liftoff points on the front, build Forts. Once you take three or 4 choice cities, the Iron or Oil usually becomes vulnerable to Para targeting, and then it REALLY becomes a blowout.
The only downside to Paras, really, is that you can't draft them. It's too bad, but if they were draftable, they could very well be overpowered.
I used to think that Paras were useless until I realized that they had the same strength as Marines, and that got me started on testing them out. Marines, of course, are great because you can move them around from Coastal city to Coastal city with great speed, attacking and taking a Civ really fast. Paras are their overland equivalent.