I will probably be around one or both days!
I'm not familiar with the post office near the airport. However, there are some other possibilities that I am familiar with: a shopping center (Lakeshore Plaza) on Sloat Blvd. in San Francisco has a post office that is open on Sundays, which I use sometimes. And the Macy's store on Union Square has a post office open on Sundays in the cellar.
In addition to those, there is supposed to be a self-service postal center in Terminal 3 near the American Airlines baggage claim area (according to the SFO website). Maybe you could hit that first and see if it meets your needs! (It might not be convenient, though, if you are arriving at the International terminal.)
Kathy