I would suggest the below, if you receive no answer and consider having enough patience:
1. Plug both contollers to the computer.
2. Make a copy of the zinput.cfg file
3. Open the original zinput.cfg file.
4. Add the below values (or replace them, if needed)
Player 2 Input
; Input Device: 0 = Unplugged, 1 = KEYBOARD/GAMEPAD
pl2contrl=1
; Keys for Select, Start, Up, Down, Left, Right, X, A, L, Y, B, R
pl2selk=280
pl2startk=281
pl2upk=282
pl2downk=283
pl2leftk=284
pl2rightk=285
pl2Xk=286
pl2Ak=287
pl2Lk=288
pl2Yk=289
pl2Bk=290
pl2Rk=291
5. Save the zinput.cfg file.
6. Run ZSnes with a 2 player game for which all buttons do something, and see if any of the buttons in the second controller work. If so, open the zinput.cfg file and write down the number corresponding to the button that did something.
7. Shut down ZSnes.
8. Repeat steps 3 to 7 (which might be what takes most time of the proposed solution), using numbers different from those you used before for the pl2...k entries until you have found 12 different numbers that make buttons do something.
9. Open the zinput.cfg file and put one of those 12 numbers as values for the each of the pl2...k entries.
10. Save the zinput.cfg file.
11. Run ZSnes with a 2 player game and see what the buttons do for the second controller. Write down what they do.
12. Shut down ZSnes.
13. Open the zinput.cfg file.
14. Notice which numbers are used for each pl2...k entry and accordingly to the notes you took in step 11, replace them with the appropriate numbers.
15. Save the zinput.cfg file.
16. Repeat steps 11 to 15 as many times needed to adjust the actions of the second controller's buttons.