Do the M/100 and L/1000 relays both fire when this happens? I suspect not since player 1 works properly. That would leave the reset paths as suspects:
Super Spin 2nd player scores (resized).jpg
The Runout switches are closed most of the time so if there were a short between the P4B and P4C switches on the Player Unit that might explain what you're seeing. If one of the score reels is 0 (e.g. 1000 or 300) do you see the problem? If not that would also point to the Player Unit since one of the Runout switches would be open in that case.

The P4B and P4C switches are on the 4th switch stack from the steel gear on the Player Unit, 2nd and 3rd switches from the bottom.

/Mark

Check the switch stack on the 100 point score unit for the second player. The top-most switch in the stack is the carry (AKA 9th position) switch. It is supposed to close only at position 9 of the score unit, and should be open at all other reel positions.

The idea is that when the 100 point score unit goes from 9 to 0, the 1000 point score unit will also advance one position because the carry switch is closed.

If the carry switch is out of adjustment and is always closed, or the solder lugs for the switch are bent over and touching, you'll get the symptom you are describing because then the 100 point score unit will be doing a carry every time it steps.

- TimMe

@TimMe's explanation is more likely. The suspect switch is in red here:
Super Spin 1000 pt relay (resized).jpg
If this switch is stuck closed or shorted the L/1000 relay would fire every time the M/100 point relay fires for player 2. The opposite however would not be true. If player 2 can hit a 1000 point target and not have the M/100 point point relay fire that would confirm it.