You can't MAKE him trust you, you just have to make your actions match your words. You can't actually guarantee him if you broke up you'd let him see your child again and you can't even make the guarantee you won't hurt him. What if your feelings change down the track? Make no such promises in relationships, they are empty ones. All you can do is reassure him you love spending time with him and you want him to be a part of your child's life and it is up to him if he wants to continue. Sometimes there are just things we can't control.
Some people are drains and some are radiators... Keep clear of the drains and hug the radiators!