While I was on the Droog website earlier I saw this which caught my eye! It's such a great idea! However, it's listed at $618!! That's way more than I'd ever pay for a swing. It's a plastic seat with a planter inside so you can grow ivy and have it crawl up the ropes of the swing. I would actually recommend Clematis as it grows like a weed and has beautiful blossoms in the spring. You could probably make your own planter swing seat out of wood. You would just have to coat it in a lot of resin so it wouldn't deteriorate over time. I think a wood seat would look even prettier than a plastic one anyway. I made an illustration of what I thought the seat would look like.
And here's a tutorial on how to make a simple tree swing. Just add your custom planter seat.
It really is a lovely idea!