that's what I did - I don't remember the exact date I met my partner's parents, for example, but I know it was in late July -early August of 2004, and we had had a hurricane come through a few days before - so I looked up the dates of 2004 hurricanes here in Florida, and guessed a date based on that. I remember the date that they left town, because the next day, we found our dog, and I definitely remember that date.
For those kinds of questions I just figured - it's not like there's a correct answer written down somewhere that an IO will look up and compare to your answer. It's not a test with a right answer and a wrong answer, you know (even if it feels like it sometimes)?? As long as you get as close to the actual dates as possible, and you actually try to figure it out, I'm sure it'll be fine. Worst case scenario, if you don't remember exactly, maybe make sure you remember the logic of choosing one date over another, in case you have to defend it in an interview.