We would need to know exactly why he was deported. You need to consult with an immigration attorney and present information about your partner's immigration history, as well as criminal history (if any). After a thorough review, an immigration attorney would be able to tell you what, if anything, might be possible. Best of luck.
It would be very important for you and your husband to consult with an experienced immigration attorney about the case. It appears that he might be eligible to apply for permanent residence while remaining in the United States, but you would need to go over all the facts and history of his time in the United States, and other issues, to know for sure. Best of luck to you.
If you do not file a petition for him, then he will not be able to obtain permanent resident (green card) status through marriage to you. Furthermore, now that you are divorced, at this time you could not file a petition for him, even if you wanted to do so.
We would need some more information about exactly how you entered the United States. But if you entered unlawfully, then the first step would be that your husband would file a petition for you.
It sounds like your husband would be subject to the Adam Walsh Act. It is very difficult (not impossible, but very difficult) to get an approval by USCIS for a petitioner subject to the Adam Walsh Act.
You will need to work closely with an immigration attorney who has experience dealing with Adam...
You most definitely need to consult with an immigration attorney about this situation. You need to obtain certified copies of all court records related to the court proceedings. Without seeing all of the documents relating to the court proceedings, it would be difficult to say whether or not your husband would be able to obtain permanent resident status. We would need to get more information.
You could make an InfoPass appointment at USCIS and request that they stamp your passport to indicate that you are a conditional permanent resident while your case is pending in Immigration Court. There is no guarantee that USCIS will stamp your passport at this time, but you could make the appointment and try.
I suggest that you consult with an immigration attorney about your case. An immigration judge can review the USCIS denial of the I-751.
You stated in your message that your husband is a permanent resident. Is that correct? In that case, if you file an I-360 self-petition as an abused spouse, you will not be eligible to adjust status immediately (because your husband is not a U.S. Citizen). So, you most likely would not want to file an I-485 to go along with the I-360 at this time.
I strongly encourage you to consult with an experienced immigration attorney near you about your immigration situation, to have the best chance...