I have just returned from the International Symposium on Domain Theory, which took place in Shijiazhuang, Hebei, China. That was a fine conference indeed. There, I met Xiaoyong Xi and Jimmie Lawson, who just happened to publish a remarkable result, related to a very recent post on coherence of dcpos: every complete lattice, and more generally every bounded-complete dcpo is well-filtered in its Scott topology. Read the full post.

With this post, the counterexample in your last post is now easier to understand. The natural numbers with the cofinite topology is not well-filtered, so any bounded complete dcpo, which is well-filtered in the Scott topology, cannot be a dcpo model of it.