In general, I don't reccomend ordering seeds over the internet; there doesn't seem to be much point when you can stop by a nursery (or, in my case, K-Mart) and pick up any number of varieties of seeds for very little money. In addition, there is the question of security issues in sending your credit card number over the internet. However, I realize that some people may live far enough from a store, not have transportation, or whatever, that would make online ordering more convenient. Below are all the options I found for ordering sunflower seeds online.

Sunflowers of Switzerland: A really wonderful Swiss company with a beautiful and easy-to-navigate web site.
Ed Hume Seeds