Annulled steel wire snare traps
These are literally the easiest traps in the world to make and set up. They work great for various small game but are especially effective for rabbits. All you need is a spool of wire (something in the 18-22 gauge range) and some basic wire cutters.
Annulled steel is what you get when you slow cool steel instead of quenching it which does 2 things for your wire. It makes it softer so you can bend it more easily without it breaking, and more importantly, it makes sure that the steel does not have any springiness; so that when you do bend it, it stays bent. These materials are something that pretty much any blacksmith born after ~400BC should be able to make for you.
All you need to do it take about 2-3 feet of wire and tie a loop into one end about 4 inches in diameter such that it can slide open and close freely. Next, find a rabbit trail and tie the other end to a tree. Because it is wire, it just kind of hangs there open in the air. Next you place a small twig sticking up out the ground just under your snare. When a rabbit comes along it will lift its head over the twig and go right into the loop. When it feels something slipping around its neck it panics and tries to run. This pulls the loop tight around its neck, and because the steel is annealed, in kinks up locking the loop tightly around the rabbit's neck strangling it. Whereas a string noose needs a spring to maintain tension, the kinked wire does not need to maintain tension because it does not release after the rabbit stops pulling.
These traps are so small and simple you can easily make 30-50 of them, stuff them in your pocket, and go around setting them all up, all in a single day.