Looking back on things tonight. One of the suggestions my DB coach gave was to occasionally invite XW along on things S and I were doing to give her a chance to interact as a friend. That was a couple months ago now and I've noticed I've tried three separate times. Each one was casual and something we were doing anyway: going to the zoo, having an Easter brunch and scavenger hunt, and, next week, his birthday party. Each one she declined and given no indication she was interested. I am trying to be patient, but I don't know what to do to encourage friendship, or even friendly co-parenting. I considered ours a close friendship when we were married. I didn't think she'd be that opposed to us interacting.
That sounds fine, that's about one invite a month so I think you're doing it without putting a lot of pressure on her. And from your description it sounds like you did do those activities without her anyway which is exactly what you should do. Ask them along with no pressure (IE, "we're going to the zoo, if you're interested you're welcome to join us"), and if they don't go then you go anyway.
When you say you don't know what to do to encourage friendship, all you can do is keep doing what you're doing and hope that XW changes her mind at some point. I know it's been a long time for your sitch, but I have a friend whose W left him and they barely spoke for a year. Then they slowly started talking again, then doing things together, and now it's been 2 years and they just started going out again a few months ago. So you never know.
