Most types of pergolas should be able to support the weight of a swing. Pergolas are often made from metal, and should be strong enough to take the weight of one or two people. If you have a wood pergola, this is also a strong and durable material that should also support your swing chair, but check the wood is in good condition - rotting wood runs the risk of breaking.
If you have joists or beams, it is as simple as tying a chain in place. The stronger the chain, the better supported your swing will be. Ropes just won't cut it, but you can also buy heavy-duty swing hanger sets, made of durable iron material that keeps your swing attached to a beam.
It's also about the strength of the chair itself. Metal swing seats don't look as comfortable and relaxing, owing to the hardness of the material, but wrapped in outdoor-appropriate rattan can soften the metal and give you a pleasant outdoor retreat.