I don't believe I've seen commercially available gutters smaller than 3" in width. Â Anything smaller than that you would have to construct yourself, perhaps by splitting a PVC pipe in half with a bandsaw. Â
<strong>But:</strong>Are you really sure you do want sloped gutters and two downspouts on a gazebo? I honestly think it's going to look rather out of place on a small structure like that. And, unless you live in a very humid climate, there won't be enough rainwater to deal with that justifies the efforts.
I would much rather deal with the water once it falls from the roof (and that's not a very high fall either). I think two trenches on either sides of the gazebo with a perforated drain tile padded with pea gravel on the bottom and both sides and covered with larger decorative rocks on top. You could also put some geotextile fabric ontop and add some soil and plants above it if that's preferred from the decorative stand point. Just make sure the drain tile leads down and away from the gazebo. Even then I wouldn't worry too much about routing the water away because it's such a small amount of water - the drain tile might catch all of it after a rain and then it'll slowly seep back into the ground.