John's got it right. I power wash homes for a living (21 years) and remove rust from many surfaces.
Oxalic acid is the way to go providing the surface is colorfast.
The acid is mild but can still burn your skin so wear good rubber gloves and eye protection.
Pull the cushions out and make sure you have plenty of air circulation in the area you are working, fumes can be bad for your lungs, a resperator is advised.
You can buy oxalic acid at Lowes , it's in most wood/deck brightners. Although the dilution is homeowner stuff it will work if you let is sit long enough.
Neutralize the acid with a base like dish washing soap in water.
Capt Brian