One tree hammock

Sink a piece of dimensional treated lumber into the ground at least two feet deep, 4x4 or preferably, 6x6. For the most secure setting, embed in concrete. This post becomes your second anchor point. Make it multiuse by hanging a bird feeder or hanging basket bracket on it.

You could always just get a stand.

I think the simplest option for your situation would be tri-pod style stand. Something like this . It would easy to build, and you don't need to dig into the ground, which it sounds like you're trying to avoid.

Basically, two tripods hold up a bar, and you hang on that bar. If you hang directly on the tripods, you'll be pulling them inward, but if you hang on the bar the force applied on the tripod is directly downward.

You might also consider a tensa4. It can be split to run 2 hammocks off 1 tree. You do have to set one ground stake per hammock though

https://www.equipoutdoors.com/products/single-point-hammock-stand