I don't think you should do that. Garen is a tank. But he doesn't provide shields or any heals soooo. He doesn't have a hook either so its just plain tank.
I'm not sure about that to be honest. While he's a lanebully in Top Lane, his spin to win is incredibly dangerous in botlane, since it's super unlikely that your opposing lane doesn't have one or two CC abilities, and you'll just die if you eat them in a row. You have no way of disengaging or actually proceting your carry. Yeah, Ulti-Nuking the opposing ADC in a trade seems fun, but I doubt it works in higher elos since you'll never really reach the point in trades where you can even do that if the opposing lane plays it correctly. I can't really see how Garen wins a lane against Zyra or Karma. You'll just get bullied into oblivion.
I've played him a couple of times as a support. He's not good, since he lacks CC, mobility and range.
It's a hell of fun to build full tank and run around annoying people though, since your damage is significative even if you go full tank. You can also deal a lot of damage to the villain, so I guess you can go for that focus.
I definitely second face of the mountain, I think it's a great tank item and a good support item at the same time. Black Cleaver stacks nicely with the armor shred from E, armor shred is nice for your teammates, and it's pretty vital to actually stick to enemies on the easily kited Garen. So I would definitely build that if the game allows it.
Sunfire Aegis is a nice splitpushing item (and stacks nicely with E again) but I wouldn't get it on support unless you actually plan to splitpush. I'd prioritize Dead Man's Plate, again for actually getting to people, or Randuin's Omen for stickiness and for peeling for carries at the same time.
It's a hell of fun to build full tank and run around annoying people though, since your damage is significative even if you go full tank. You can also deal a lot of damage to the villain, so I guess you can go for that focus.
Go Relic Shield into eye of the equinox so you can build full tank items ASAP. Probably Sunfire Aegis; either Boots of Swiftness or Mercury's Treads; Dead Man's Plate; Spirit Visage and a last item of choice depending on the game (I usually bought Black Cleaver or Turbo Chemtank for the cheese).
There's probably more optimal builds depending on the game and your playstyle, but that one is the most balanced one IMO.
Sunfire Aegis is a nice splitpushing item (and stacks nicely with E again) but I wouldn't get it on support unless you actually plan to splitpush. I'd prioritize Dead Man's Plate, again for actually getting to people, or Randuin's Omen for stickiness and for peeling for carries at the same time.
EDIT: I'd probably consider building Locket of the Iron Solari over Spirit Visage as well, though then the build would start to be very selfless indeed.