Everybody has coffee mugs
tote bags
refrigerator magnets
I can’t think of anything else to suggest without knowing something about your comic. Is there some item like a particular desk or chair or pencil holder always in the frame?
I can’t claim any knowledge about potential suppliers either, but perhaps another webcomic author would able to point you the right way? From my uneducated perspective, it seems like many online artists truly do their best to answer a huge volume of fan mail, and appear to be the people who would be happy to help out.
It might also be worth it to call the organizers of any decently-sized webcomic convention…perhaps they are familiar with vendors who advertise their services at the conventions.
I’ve been following it since Jonathan originally mentioned it, and I’m not sure what merchandise would have appeal, necessarily. Last Res0rt has character-themed bottle openers, of all things, but I don’t think the characters designs are really distinctive enough for that. Still–maybe character/popular scene bookmarks? Like one with the brownies chasing Key with a flyswatter?
Once you have a reasonably loyal base of readers, why don’t you try and organize a Kickstarter (if you are in the US) or Indiegogo (if your are outside the US) campaign to raise enough money to do, for instance, a print run of your comic?
I am sure that it shouldn’t be too difficult to find a printer to do a print run of your comic. Besides, by what I see, your comic is B/W – that would make the printing cheaper!
The only problem is volume --you need a minimum number of copies to print, and it can be expensive. But going for a Kickstarter or Kickstarter-style in order to get the initial capital is always worth trying!