"Can't" is a huge pet peeve of mine, so it doesn't enter into my vocabulary unless it is real, as in, it is
in fact or in all ways ultimately impossible that ____, in which case, I usually term it that way anyway.
My dh says it though, and has asked me what he should say instead, and honestly, the most useful advice has been that if he's about to say anything involving 'can't' to another person, it's best just not to say anything at all. On some occasions, it can be helpful to offer help, but mostly, if someone actually believes s/he can, then s/he is likely correct or will figure something else out without the interference of a discouragement.
He was also using it to express his preferences, such as instead of saying "I would prefer that you not sit on the back of the couch because it is not built as a seat and will wear out quickly if we use it as one. Please sit on the seat," he would just tell our dc that they can't sit on the back of the couch. Obviously that's not true, since they did, even when it clearly irked daddy. So, now he states his preferences, and dc are far more responsive because it no longer even matters if they share the same preference, they are usually willing to concede on small issues because it doesn't much matter to them either way, and negotiate on bigger ones.
"Don't" is admittedly a harder one for us. My strategy for limited use has been instead to reframe what I am actually hoping for after stating my observation constructively, not to degrade or express frustration, such as, "Sweetie, you're dropping your food. (pause so they can take a second to look and see the same thing) Please try to keep your food on the table/plate" or "Sonshine, you're yelling and my ears are hurting. Please lower your voice."
Of course if I can't say these things kindly, sincerely, then it may not be as helpful as it seems it could be. I have found there to be a pretty enormous difference in the ability of my children to self-regulate with this style of communication over times when I've slidden and had "don't-days."

We've been on a four month hiatus in the bush and it is so nice to be reminded of little practical things we do and and encouraged in our values here again. Thanks for the great topics!