Hammocks are fine. It's recommended you get some made out of fabric instead of the mesh as to reduce the risk if their claws getting stuck in it. I bought a mesh hammock before I knew any better, so I just lined it with a fleece cover after the fact, and she's never had any issues with it.
It's also super easy to make a hammock out of fleece. Get some strong enough suction cups with hooks, and some fleece. Cut the fleece to the shape and size you want. Snip some holes in the corners and stick the suction cup hooks through, and hang it up! If you want to reinforce the corners, you can also get things like eyelets or grommets as well (probably unneeded unless you have a hefty dragon). You can also use lighter fabrics like cottons and flannels, but you'll need to hem them as they'll fray otherwise, and the corners will need reinforced or they'll tear eventually. Fleece doesn't fray, and is sturdier, so it's less of a hassle to work with.
They also make hammocks for beardies made of woven seagrass, but they tend to be on the pricier side, and I'm cheap. I've heard decent things about those too though.