I agree with Warren.

The important thing here is spreading the load. In theory you could have quite thin tubes and it would stay intact, even perhaps pultruded tubes.
However, in practice this wouldnt work. As you know the load (or kids in this case!) will move around, bounce up and down etc etc. Not to mention sitting on the edge of the hammock and causing a point loading force.
Although pultrusions are generally stiffer down thier length due to all the fibres in one direction, this leaves them weak when it comes to point loading. So what would happen is it would be fine while they are on the hammock laying down, then if one sat on the edge, the tube would snap due to high point loading.
Hence this is where roll wrapped tubes come in as they have fibres both down the length of the tube and across it meaning they can resist point loadings far better.
In terms of specific tube sizes, our
RollWrapped Carbon Fibre Tubecome in several sizes but are all sized by thier internal diameter as they are mandrel made. We do specify the outside diameter but this can vary slightly due to manufacturing process and tolerances.
The closest we have to your initial ideas is a
22.2mm ID Carbon Fibre Tube which has an O/D of 25mm. That should be reasonably stiff for you.
Even if you dropped down a couple of sizes, it would unlikely break although the tubes would bend considerably.
Warren PenalverEasy Composites / Carbon Mods - Technical Support Assistant