I moved form California to Maryland with my son almost four years ago. His biological father/ my ex-husband definitely tried to fight the move in theory and made the process more difficult than it needed to be, but ultimately if you take out the emotional stress, it was pretty simple.
His dad had supervised visits once a week when we lived in the same city. He wouldn't simply stipulate to my move-away modification, so we went to court. The judge made it clear that it was my right to move and as DS's custodial parent, the assumption was that he would move with me. The task was then to plan how DS would maintain a relationship with his father from across the country and how/when he would be available for visits. I suggested regular Skype and his dad visiting here as well visits there when we visit family once a year for a week.
If you have a legal custody agreement, and the terms of that agreement and you are moving too far to maintain the terms of the agreement as they are, it has to be modified... you'll have to file for that... that's where your ex can decide to cooperate or not. He can't stop YOU from moving. He can TRY to stop you from moving WITH your son. But if the current arrangement is that he sees him once a month, and you have a clear plan about how you'll support them maintaining their relationship in a similar way after the move, no one's going to say custody should transfer to his father (which is the only other option, right?)
My advice would be to phrase it in terms of when you'll make your son AVAILABLE to his dad, not that you will ensure he sees him at those times. It's semantics, but it's made a difference in my case since his dad hasn't seen him in over two years because he doesn't make arrangements but
When you bring it up to him, do it in writing (email) "I'm thinking about moving to Mass. Since this will impact your time with ____, I wanted to plan with you while this is still in the early stages. What are you thoughts? ... and keep all conversation on this topic documented that way so you don't run into a he said she said.
Hope this helps.