A long, long time ago I bought one inch strapping that is used as patio furniture recovering. I have no idea if it is still available. I left in the sun to soften and pulled it taut. Too taut, bent the frame in a bit! Looked fine, lasted as long as the original cover.

Could easily use rope, maybe clothesline, maybe 1/4" in size but it would take a lot of it! If the rope is stong enough could wrap it around the frame a couple times for each time across to use less. Wrapping from top of one side to bottom of other makes a decorative weave look without any actual weaving.

Not sure if the books are still around but I did a search and heres what I came up with. Looks like a fun project. And could really make a colorful patio.

Mary

PS. I looked alittle closer to the pics....zoomed in on them..and I think these are really more of a weaving then macrame. But still nice.

Here is a link that might be useful: macrame chairs