It is possible to replace a broken recliner spring, but the process is fairly difficult. Upholstery Resource recommends taking the chair to a professional to be serviced rather than attempting to do it at home.
To replace the springs, begin by taking the back, seat and all additional padding off the recliner. Locate the hinges that hold the spring and take out the bolts. It is possible to remove the broken spring and replace it with a new 9 gauge zigzag spring. Measure the spring before placing it; it may be necessary to cut it down to size with a pair of wire cutters.