Drop the rope
I've been there, I bent over backwards trying to ensure my daughter still had a relationship with her dad at great cost to myself financially and emotionally and ultimately a too high cost to her emotionally.
We split when she was 2 and immediately he became disinterested and unreliable.
Now over 20 years later I have so many regrets.
I cut him off, he took me to court, not because he cared for dd but because he hated me cutting him off, taking the decision for him effectively.
There were several hearings in the end because he consistently didn't hold up his end of the bargain.
In hindsight I wish I had passively let him vanish from her life. If I had not proactively pursued contact with him for her, I believe he would have relatively quickly just stopped bothering.
What happened was this is what occurred when she was high school age which was far harder for her to deal with that rejection.
She's now an adult, she got back in contact with her half siblings a few years ago on SM but her relationship with her dad is beyond repair.
He now wants a relationship with her, still on his terms (she lives near him but he only makes an effort on certain occasions eg his birthday, but not hers) and throws a strop when she won't play along. Well you reap what you sow!
Over the years I have naturally come to know other single parent families and noticed there are 3 potential outcomes:
Non resident parent remains engaged and reliable and a good co-parenting relationship works for all concerned.
Non resident parent is absent. Child quickly gets used to this and they are their own wee family that usually works well.
Non resident parent messes about like my ex and your baby's dad and the kids end up suffering massively.
Hence - drop the rope.
Don't antagonise him. Don't fight for contact, or against on the rare occasion it does happen but also don't hang about waiting for daddy for hours, if he's more than half hour late go be somewhere else that he can't turn up to. Natural consequences for him.
I think you'll find what will happen is he will naturally disappear from your lives within months.
At which point just forget him, move on and raise your child the best way you can.
I wish I'd done that, the pain my daughter feels at being wayyyyy down her dads list of priorities is heartbreaking. Though these days she's more likely to get annoyed/angry/irritated eg we planned Xmas together (she lives away for uni at mo), 9pm Xmas eve he calls asking what time she'll be over tomorrow - he hadn't been in touch with her since before Halloween! But just assumed she'd be there for Xmas. He then took umbrage when she said she was spending it with me to the point he was like "well you're not getting your present then" 
dick!
Her response was "fine whatever"
Your baby needs consistent and reliable people involved in raising and supporting them, not someone who doesn't care enough to even just show up!
I do agree with CrunchingLeaf that keeping records of it all is a good idea cos if he and his gf split he may try crawling back and if he does decide to take you to court you'll want evidence of this inconsistency.
It's one thing I did and was glad of, texts and emails showed the court my evidence of his flakiness. By the time of the last hearing the judge was like, this guys over the last 2 years repeatedly flaked out, nah. Very rarely in a case with no obvious abuse (I would argue this is emotionally abusive) the judge actually said to my ex if he took me to court again and we were there cos I'd stopped contact due to his flakiness the court would terminate his parental rights and he was entering that into the record for future ref. Even my lawyer was shocked and said that hardly ever happens unless serious abuse occurring.
He actually wasn't seeing his son when i was with him they'd split a while before and he was going through court for Chile cus5ody he didn't see his son for 2 years as he told me she stopped him seeing his child so he had to apply to court
Sorry to say but, you knew what he was like then. Why expect him to be any better to your child?
he will disappear and complain about you to the next mug woman he gets pregnant
Yep