This was/would be the second one I would have to change.
Should I use was or would be? And why?
Either option is correct, depending on what you want to say. Both take place in the past.
This was the second one I would have to change.
This sentence means this event definitely happened in the past. There was a point in time when you realized you would be forced to do something. For example, you just realized your car got a second flat tire that you would now have to change.
This would be the second one I would have to change.
Would be is also past tense, but it's conditional. The narrator does not yet know if the possibility is true or not. In this case, she may have run over some nails on the road and has just pulled the car over to check the tires. If there are nails in the tire, this would be the second tire she would have to change.