Basically, I’d say swag [i.e. merchandise] is a good way to generate income. and increase visibility.
As to how to proceed, things may be more or less complicated, like fair trade/sustainability concerns, but aside from the logistics, I’d assume that tasteful graphic design would be the most significant attribution to make such an undertaking successful.
I’m not sure why swag is the word here, and slang dictionaries do not help my poor english knowledge. But despite the linguistic inconveniences, those lovely items can be used as advertising on all sorts of tournaments and go convents. I don’t think Go community is large enough to make some real revenue stream, but long term they would be definitely a great way of bringing new players in, hence increasing main revenue stream.
At first I also had difficulty understanding the word, but then …
swag - Wiktionary, the free dictionary (not a slang dictionary, but yes, coming from thieves’ slang 
)
#2, stolen goods, booty, (or “loot”, “plunder”)
Like people also say “it was a steal!” even if they didn’t really steal something, just meaning they got good stuff for cheap.
When I get discounted products at the local supermarket because they had reached shelf life I also say “I made booty” 
I guess “swag” would be a lot better, of course, than just some dairy products, rather like gold and silver and gemstones.
Or … OGS-branded mugs and T-shirts, OGS lanyards, coasters, caps (like, “MAKE GO GREAT AGAIN” ), any branded paraphernalia, all kinds of things which, to OGS lovers, would be just as valuable as gold, silver, and gemstones 
I think I can imagine wearing a beanie with the OGS logo and “MOGO”
My thoughts on the four possible revenue streams:
Advertising - I don’t have anything to say about this, as I’m a site supporter and so don’t even see them.
Site-Supporters - I made a suggestion on another thread that was liked by one of the devs, so I hope that meant they’re going to work on it. My idea was to display whether a user was a supporter wherever their name appears on the site, on the game page, in chats, in game lists, etc. Basically, wherever you see “Username [rank]”, it should be enhanced to be something like “Username [rank] *” for supporters, where the * is some symbol they devise. The text, “site supporter” should appear when the symbol is hovered over, and clicking the symbol should take people to the page where they can sign up to be a supporter. The idea is to make every player more conscious of the existence of the support option, to make it easier to click through to the signup page, and to make it more attractive to be a supporter by identifying supporters as such everywhere they appear on the site.
Swag - I agree with others that OGS should not invest in production and inventory and fulfillment, etc… Instead, they should use a service like Cafe Press or Zazzle to create branded products they can earn royalties from. The profit would be lower, but would carry zero risk and require minimal effort. Start with a single graphic, make it available on the full range of possible product types, and see how it goes. If it sells, begin creating more graphics.
Books/products - Partnerships with Go book and equipment sellers might be possible, but the low hanging fruit would be Amazon affiliate links. I would think that in a single afternoon, someone could identify, say, the two dozen most popular Go books, and maybe a few boards and stone sets, and create affiliate links for them. Then maybe another afternoon to create a simple static page full of Amazon widgets for each product. Then see if OGS members use them. If not, don’t do any more. If they do, then add more products and create a more robust product management system that allows searching and categories, etc.
All my suggestions share the quality that they involve no risk and minimal effort. They should all be done right now, and then we can see where we stand.
In response to your second point:
This is already implemented (in part). Site supporters have their names in yellow everywhere on the main OGS site and in the chat room they have a yellow orb next to their name as well (both of these have the option to be turned off, but are on by default for all supporters).
When you visit their profile page, under their name in big letters is “site supporter” with a star either side of it.
The only aspect they have not implemented is making this label a hyperlink to the “become a supporter” page.
Seems to me that the most obvious prefered situation is just a bunch of supporters.
For that to be more effective i think there should be more bling for the supporters.
Like maybe limiting namechanges, discount-deals on stuff/partnerships or something.
ive always lked that idea of having x amount of “bombstones” a game, where you can place a stone and trigger a little nuke or bomb-animation. Perhaps used when you play a nice tesuji or kill a group . say 3 per game or something. that would be fun =) and wouldnt break the game.
the point is; more value for supporters
I’m okay with giving supporters cosmetic, non-gameplay affecting stuff, but being a site supporter should still feel more like a donation than a “premium subscription”, and not paying shouldn’t feel like you’re a second class citizen. So none of that “analysis/conditional moves/score estimator/zen mode/etc. only for site supporters” or “X free days then pay up” stuff. That would be a surefire way to drive out majority of the players.
Oh wow! I never noticed that for two reasons:
There are so few supporters that I guess I’ve never run into one, and the fact that my own was in gold led me to erroneous conclusions about its meaning, if I bothered to think about it at all. (Players see their own names in gold, each player’s name is in a different color, etc.)
There’s no explicit symbol or hover text, which is absolutely key. Otherwise, you depend on players already knowing what the gold means, but the whole point of the symbol and hover text is to spread awareness of this very option.
But this is good news, because it means OGS can enhance the power of what they’re already doing significantly with just a very minor tweak.
how about one double move when playing non-supporters 
would totally buy an ogs sweatshirt but it’d need to be cozy 
go turns pay to win? 
A bomb animation for killing groups? I have no problem if two players agree to that but I sure do not want it in most games… I might as well migrate to Fly or Die…
A number of people have mentioned a one time payment option. I think this should be looked at. I would consider it. But I do not care for monthly withdrawals.
And something I have not seen is how much money would it take to increase foreign servers and other upgrades? And how much would it be divided among regular users?
New, site-supporter only feature for making own custom theme by simple “Backround color: #ff0000” type of tool?
Soooo, if we want some merch, how about helping make it happen? 
I am sure there are some graphic designers among us that could help making it easy for OGS to make this whole thing happen…
Let me start:
I had a cool idea for a t-shirt:
Inspired by the Patagonia t-shirts. Not sure if this constitutes as copyright infringement 
I made this, looking forward for the European Go Congress 2018 where I hope to meet some other OGS User:
How about live tournaments with a small entry fee and potential (cash or otherwise) prizes?
I mean, that’s how the American Go Association gets a good portion of its money (other than selling memberships)
And site supporters could get a certain number of tournaments (at a lower cost than them buying tournament passes individually)
Cool idea but I still really want OGS t-shirts <3
Two words: fidget spinners
