Fiber Ropes
A fiber rope is probably the most common and recognizable rope used for tire swings. Manila and sisal are good, strong fiber ropes. Ropeswings.com recommends going with sisal to avoid manila's tendency to rot and break with use over time. Using a rope at least 1 inch thick provides a good size for hand gripping, safety and durability. Ropeswings.com also recommends coating your rope ends with rubber or whipping to keep fraying at bay.
Mountaineer's Climbing Rope
You may want more give, style or bounce to your tire swing, in which case you could use a bungee-type rope, or mountaineer's climbing rope. Many forms of this rope, like Dynamic Rock Climbing Rope, are strong and durable; however, many sizes are too small for a comfortable, safe grip. To avoid hazards such as slipping and rope burn, get a larger size bungee cord for your swing. If you hang your tire swing from a tree, Landscapingideasonline.com suggests you put a piece of rubber hose around the portion of the rope that will contact the tree limb to prevent deterioration and damage.
Chain Rope
Although some metal chains do rust in the elements, they are still a viable option to use as rope for your tire swing. According to Treetopbuilders.net, cables or zinc plated chains are best for resisting the damage from exposure to UV rays and moisture. A lot of wear and tear can come from the grinding of metal on metal with these ropes on tire swings, requiring more frequent replacement. However, with careful maintenance and a watchful eye, accidents can be averted. For longevity with chain rope tire swings, Treetopbuilders.net suggests purchasing the correct swing hardware for installation.