Sorry for your loss, Brandon. I've been looking around. It sounds more like a movie than a show. The kind where the cowboy befriends a kid/teenager and then has to leave, and Dad doesn't approve of the drifter lifestyle. My first thought was Shane. My dad is close to the same age as yours (1961) and he remembers watching Shane as a kid with his dad. But that would be too obvious. It still doesn't sound right.
Could it have been a Hopalong Cassidy movie? They could have been showing them in the 60's and 70's. "Don't watch him ride out of sight or else you'll never see him again," sounds sentimental. Like, "The man will always be in your memory."