Sounds like the coin chute switch is able to activate the Start relay (S). A switch on the Start relay will decrement the credit unit.

If the left coin chute is used, it activates the Start relay directly, without adding credits.

If the right coin chute is used (if it has one), then it can be set to add credits without starting a game. I'm guessing you used the left coin chute though, which would take away a credit if it had one.

The replay button should also activate the Start relay, but there are a couple more switches involved. The difference between the replay button path and the left coin chute path is that the replay button path also needs a normally closed score motor switch (usually motor 1C), and the Zero position switch on the credit unit needs to be closed.

The zero position switch would normally be closed when there's at least one credit on the credit unit, but it's possible it's not fully closed yet at position 1, or the contacts are dirty. So that would be worth checking.

Otherwise, check the score motor switches at position 1C (but check your schematic at the bottom to see exactly which one).

Excellent. Enjoy the game!