Is it okay to contract were as 're?
I was not here when you're saying I'm sorry.
Is it okay? Or at least okay for informal use?
Also, should I use quotation marks with I'm sorry
No. English speakers will always read "you're" as "you are", never as "you were".
To your second question: You may quote but it changes the meaning. Without quoting it means the person was saying that you are sorry. With the quotes it means they were saying that they were sorry. To see the difference, consider the following situations that could arise among three friends who the previous day had some kind of argument. In each we are standing in the same room we were yesterday during the fight.
In the first, you claim that you apologized for your part in the fight, but the other friend denies that. So you turn to me to ask me to verify that you did indeed offer an apology. Unfortunately I had stepped out of the room at the time and I didn't see that part, so I respond by shrugging and saying:
I'm afraid I can't say either way, because I was not here when you were saying "I am sorry"
In the second situation, you now claim that I am in fact to blame for the upset, that you explained that to our friend at the time, and that I clearly accepted responsibility because I didn't object when you told our friend how bad I felt. But again, I call on the fact that I wasn't in the room:
Look, I was not here when you were saying I am sorry, and that's nonsense anyway. And the next time you want to apologize on my behalf...well please don't!