Welcome, I am Cory.
Do you pay monthly for AOL?
Unfortunately, AOL does not have an online tool like other email providers. The only way to get the address book back is to have AOL go into the server and retrieve them.
Because you pay monthly for AOL, they will help you do this. You can contact them at(###) ###-####and tell them that the account was hacked and you need your address book recovered.
I hope I have answered your question today.
Please do not forget to look for the stars at the top of the question to rate my answer to give me credit today.
Please let me know if you need further help with this.