Should a man have rights to his unborn child?

❄️Sara❄️
My SIL is almost 6 months pregnant. She has a "friend with benefits" that is the father. My SIL is 26, a single mom to a 10 year old and is living with my MIL and FIL. I love her to death but she's had a lot of trouble getting things together in her life for herself and for her daughter... so it was a bit of a shock when everyone found out she was pregnant. It's not an ideal situation for her right now but everyone has been supportive for the most part. 
Her parents told her she could only continue living with them if she did not include the father of this baby in their lives. My SIL agreed and has gone to extreme lengths to keep the father out of the picture. Now the thing is that he truly wants to be a part of his baby's life and part of my SIL's pregnancy. He happens to work at a place near where I live- so I see him regularly. He's begged me multiple times to talk to my SIL for him, he's given me notes for her, asks me for her new number, etc. My husband and I agreed that I would stay out of it so I mostly just listen to him, I don't give her the notes or give out her number... but I have to say I feel bad for the guy! He genuinely heartbroken over the situation and so is his family. He told me that he spoke with an attorney about this and there is nothing he can do until after the baby is born. Here is a guy who wants to do the right thing and wants to be a part of his child's life, wants to see him grow and be born but he has no right to do so at this point. Should men have more rights when it comes to an unborn child in situations like this?