You're in a tough spot...and I've been in that spot. I was 28, in a relationship with a man who was 39...very similar.
I can almost guarantee that if you decide to spend your life with this man, you will resent him in the long run. I'm sure he's a great guy (otherwise, why would you have stayed with him for so long?). But when you and your partner want different things, that means that one person has to give up what they want, in order to maintain the relationship. That isn't compromise, that's giving up a part of who you are.
And I can almost guarantee that HE will feel inadequate every time you are in the company of children, see a baby on television, in the grocery store, wherever. That will lead to him feeling guilty and generally pretty rotten about himself. He's the other half of this relationship so don't forget about how it will affect him too.
It's possible to love someone, but not spend your life with them. I gave up my great guy who didn't want children about eight years ago and, although I still don't have any, I'm still happier than I would have been, spending untold amounts of energy to try to change his mind. He's married now and still doesn't have any children, so I know he didn't lie to me. Even though I was incredibly disappointed, after a while, I realized that we wanted two different lives, and there was no middle ground.
On the other aspect of your relationship, if you have been with him for three years and he isn't prepared to make a permanent commitment to you by this point (his also being 36), then it's highly unlikely that he'll make one in the future. Of course, he's the one who will be missing out on a wonderful woman. But you are better to take the time now, at 28, to heal your heart and reinvent your life, than to look back at 38 and regret time you've wasted trying to make him do something he doesn't want to do.
If he really does want to spend his life with you, let him work for it. Let HIM pursue YOU...it sounds old-fashioned, yes, but men are hard-wired for the pursuit, and we're hard-wired to BE pursued. Ever wonder why the number of single people in our generation is so much higher than our parents'? I'm not talking about playing hard to get. I'm talking about letting him be the man that he was created to be. If he still pursues you and works hard enough (by YOUR estimation...leave the girlfriend peanut-gallery out of it), and you feel he's sincere, then you can let him know that you still want to spend your life with him, but only with a PERMANENT commitment from him (for me, that would be a ring, for you, it could be something different). But by no means should you EVER try to "seal the deal" by having a child. That puts your child in a position to be the tie that binds, and that is NEVER fair.
And finally, why not pursue some counselling? People always think that counselling is only reserved for people with serious problems. Imagine how fewer serious problems there would be if we got advice BEFORE a crisis comes up! If you belong to a church, you can get counselling from a pastor or priest, or if you prefer (but there's a cost involved), find a marriage counsellor and go for a few sessions. Marriage counsellors are not just for married people. They can also help you identify issues and resolve them BEFORE making a permanent commitment.
I went for counselling with my last boyfriend and I found out some pretty surprising things, things I decided I couldn't live with, so we broke up. Sure, I miss him and it's awkward (because we attend the same church and belong to the same social circle), but we'll get past that awkwardness in short order, compared to what it would have been like if we'd have made the mistake of getting married and then divorced.
You seem like you've got a good head on your shoulders, so you'll do the right thing. I hope this has been helpful. I wish you the best.