You can buy inexpensive FM Stereo transmitters that should work well enough for basic testing. I have seen a kit for one that just does the FM Stereo multiplexing, but I don't know if your RF generator actually supports FM modulation at sufficient rate and depth for this. My HP 8656A does not, for example.
If you want something more accurate or adjustable, you need specific FM alignment equipment from someone like Sencore or the like. My R&S CMU200 has a basic FM Stereo output module, but it doesn't have the capability of being modulated by an analog input, so it is limited. In conjunction with a cheap FM stereo transmitter, I get by.
Synthesizing the signal yourself well enough for calibration, adjustment or just high-quality broadcast is a lot easier said than done. You have to generate a 19kHz pilot tone and then a sideband suppressed amplitude modulated 38kHz subcarrier that is exactly in phase with the 19kHz pilot tone. The main FM carrier is modulated with the L+R (mono, combined) signal and the subcarrier is amplitude-modulated with an L-R (difference) signal. There were custom chips for doing this, like the ROHM BA1320 or you can look up kits for FM stereo encoding or multiplexing. Some of the methods used are cruder than others. This would be a pretty deep dive to just fix one receiver.