Insert eyebolt into steel tube without using nut?
What can you get at a typical hardware store?

Rather than focus on that one hole that you do have, look at other types of hooks.  They have eyelets that are fixed onto metal plates.  These plates can then be screwed to the pipe using some self tapping sheet metal screws:

  

Harder to find, but another option...

There is something called a rivnut, and as the name suggests, it is a cross between a rivet and a nut.  You can secure them from one side only like a rivet, but they have a threaded hole that you can then thread an eye bolt into.  They require a special tool to insert them, and you'll probably have to drill the hole that you have bigger to accommodate the outside diameter of the rivnut.  If you only have a few to insert, you might be able to get by without the special tool.



Low strength option

If this is light duty, and the metal of your post is thick enough, you might be able to cut some threads in it with a thread tap and correctly sized drill bit. You'd only get maybe one good thread cut into the pipe, but that might be enough if what you're holding is light enough.  You could also force an eye bolt with wood screw threads into the pipe.  Again, not very strong at all, but might work for you.