I've built my share. Here's one:
Apologies to John Anderson :D My daughter Meagan wanted a swing for the backyard where she lives while at school. The weather and travel slowed me down a bit; one more coat of finish and it'll be ready to hang. Happy Belated Birthday girl. Gary
www.penturners.org
I made it without plans; took numerous hours to mill all the material, drill and get the frame together and screw the slats on.
Probably half a day for the first one.
A simple unit made of pressure treated wood would be a good start.
Two things:
You need a curve in the seat and the back.
Most builders get the seat curve right but do a straight back which isn't comfortable.
You want a curve which provides lumbar support. The curve in mine is subtle but very comfortable.
Here's an example from LJs.
It also appears to have a good curve for lumbar support:
Robert2014's Project
www.lumberjocks.com
The one I showed above was built in 2007.
It's been repaired and painted and is still in use out in the weather today.
In fact, this morning it was loaded into my truck to relocate it tomorrow.
It has an A-frame made of 4x4 posts and a 2x6 header so it can stand by itself in the yard.
You could offer the A-frame as an option for those without a structure to hang it from.
Once you get your pattern for a comfortable piece, you can start making more expensive ones using nicer wood.
Good options are white oak, mahogany and IPE or similar long lasting timbers.