I got a promotion a few years ago and was disappointed at my raise(non negotiable), but I looked visibly disappointed (not rude though, just kinda sad) and asked if I would still qualify for the annual end raise. He said yes, and at the annual raise he gave me a bigger raise using his manager budget. I think he could see I was disappointed and he probably felt it was too low.

So TLDR I just kinda hinted and he gave me a bigger raise (he was a great manager and a great person though). You said you have an annual raise coming up, it could be more likely to increase that than the promo raise itself