You mention that your boyfriend has a worldly attitude, but then so do you. If marriage is simply "a piece of paper" to you, then you have a worldly attitude. If you commit yourself financially, such as signing a lease, to a man that you are not married to, then you have a worldly attitude. If you want to marry a person with an awful attitude who does not follow God, then you have a worldly attitude.
I understand that you have made choices for financial reasons. But that is not the way of God. When you willfully reject what he says about marriage, and continue to do so when you know what He says, then you have rejected Him. And while He still hears your prayers, I can't think of any examples of Him blessing someone who is rejecting Him.
I also understand that you have gotten yourself into a situation where there are no good alternatives. Unfortunately, we all have to suffer the consequences of our ungodly choices. At this point, I believe that the prayer that He will hear and honor is one of repentance and commitment to follow His leading. That means that you put His will above your circumstances, and are willing to follow His guidance and stop living in a manner that is clearly displeasing to Him. When you die to self, He guides you. But when you manipulate things your own way, He removes His hand and allows your free will to experience what ever consequences follow.
On another note, why you could possibly want to marry someone with such a bad attitude is beyond me. To choose someone who is ungodly, disrespectful and angry, and then want them to change is always a sucker bet. If you are wise, you will go to God and give the entire situation to Him, and be willing to walk away from this (based upon what you've said before) toxic relationship.
So then answer to the question of how to pray when you're cohabiting, is to pray, like Jesus, "not my will, but Yours".