If all the fasteners in the frame are thoroughly tight, put a drop of 3-in-1 oil on the end of each spring where it goes through the eye and contacts metal (two on the upper end for each side) and see if that gets rid of most of it.
Squeaking is caused by metal-on-metal contact where there's minute movement and no lubricant. Changing out the springs won't take care of where the squeaks usually come from.
After lubricating the spring ends, if it's still squeaking, have someone sit in the swing and observe the bolted joints for slight movement. If they're reasonably tight, you might hit them with something like Tri-flow lubricant spray between the joined pieces and wipe the residue off. The spring coils wouldn't be hurt by a little of that either as an anti-corrosive.