Reddit mentions of Delta Education 13 Dram Plastic Vial with Lid (Pack of 10)

Yes, you are correct that it still illegal to ship live ant queens through the mail, or at least it's a grey area.

I actually had the exact same problem when I started in the hobby. I learned that I would have to capture my own queen and quickly gave up on the idea. The next year I was swimming early in the morning and saw a bug land in the water, then another, then another. I then found the forum formiculture.com and asked for help with identification. Sure enough they were all queens that had just mated mid flight and flown down to find a suitable spot for a founding chamber.

Since then I have found more queens than I can handle and I realized it's way easier than I had previously thought. Most of the time I'm not even looking.

If you are anywhere in the northern hemisphere, right now is most likely a perfect time to find queens.

Ants Canada has a ton of videos that can help you get started like this one. As you can see, he just walks around his neighborhood in the summer and finds them fairly easily.

I recommend using plastic pill bottles to collect them.

With all that being said, you absolutely can buy queens, you just can't ship them. Check out http://www.antscanada.com/queen-ants-for-sale/ Also ant forums (I prefer formiculture.com) usually have plenty of people selling queens locally all the time, or even selling/donating full colonies.

If you (or anyone else) has any more questions about the hobby, feel free to ask.

I think what you're looking for is a "plastic vial"?
Maybe something like this