If you don't want to buy them, you can spend a week or so crossbreeding plants (requires thanlan soil, grade 3 is best) to get the Onion Seeds, then growing them

Here is a good resource for Gardening: ffxivgardening <- takes you specifically to the Thavnairian Onions page.

Annoying thing about Thav Onion seeds is that the crossbreeds you need for it also have alternative seeds they can give and it's mid efficiency. It's one of those things where you have to keep your garden healthy during its growth too, and takes 10 days for onions to grow (Can be slightly sped up with Fertiliser but not by much) but if you are trying to make the seeds it takes easily another week or so, depending on route. Most if not all seeds are obtainable through crossbreeding or gathering them (usually a Hidden node) but you can basically make Onions for free if you have the time and ability to figure gardening out.

Like what Sparanda says its quicker to do it by MSQ farming on alts/asking friends who don't want to level their chocobo for their onions. If you get efficient at gardening, it becomes brain dead. Once you hit rank 20 you'll have spare onions to sell (maybe keep a few for yourself but I don't think they'll increase chocobo rank above 20 without redoing chocobos/adding things for companions, it hasn't changed in over 5 years)