You're very welcome.
The open line show is on VOCM. They have a website. The morning show is from 9 to 11:30 AM NL time. The afternoon show is from 2 to 4 PM NL time and there may be one in the evening, too, but I'm not sure about that. There is a toll free number from outside the province but I don't know what it is. It should be on the website. I believe you can also contact the hosts via e-mail from the site.
The local newspaper for St. John's is the Evening Telegram should that be of any use.
I think part of the problem with this missing man is that it is so long ago plus the fact that word didn't get around like it does now. It's possible he has no relatives alive, too. Back then, I doubt the police put much time into the disappearance of a grown man. Also, depending on where he came from, maybe the resources just weren't available-especially in a small place.
If you know this man's name it may be possible to track his family down through genealogy.