PS: Note this is a LONG explanation - sorry.
PPS: Also, i was really excited when i thought of this, so sorry if it has been said already, i couldn't find it via search.
Ok, after reading some of the forum (using the search tool for "underwater base"). i saw some comments on begin sad about not begin able to dig underwater, i MAY have a solution for this.
You'll need an infinite source of water - such as a river or ocean.
Dig your fortress the way you normally would, above ground or underground, doesn't matter.
Now, you have to wait for the trade caravan to see where it spawns, then build 2 GIANT long walls from your trade depo to the spawn point of the caravan making sure theres enough room for them to pass each other and whatnot. (cant draw a pic since i'm not sure how to do so in here)
find the infinite water source and make some kind of auto-pump system, pumping the water from wherever it is, to the top most part of the map. (you could probably use Blocks/Walls to build it higher) so that when turned on, the water would eventually flood the entire world(usually a bad thing). BUT DON'T TURN IT ON YET.
Then, making sure your fort is totally self-sustainable (as in, not needing to go outside. ever), build a roof over your wagon pathway, make sure no part of your fort has an exit, Turn on the pump system and bring all your dorfs inside.
Tada! your very own underwater base! with the ability to trade with caravans!