I buy this from amazon: https://www.amazon.com/Bonka-Bird-Toys-Cockatiel-Accessories/dp/B07NVRS9NV/ref=sr_1_48?crid=12RFEI8J1B8GM&keywords=seagrass+mat+for+birds&qid=1654013166&sprefix=sea+grass+mat+for%2Caps%2C104&sr=8-48.
It's three mats connected by metal rings that you can pretty easily...
I have that same hammock for my budgies! They really love it, possibly a little too much, because I constantly have to replace the seas grass mat, lol.
I don't have a conure (although I would love to have one someday). But my favorite species is probably the Emma's conure. They're not generally kept as pets, but they're gorgeous. I really like GCCs and Black-capped Conures too.
I do have 2 budgies though.