I'd just like to bump this because I'm going mad trying to think of the same show. It was not Pappyland, but there was definitely a farmer, and he would ask kids to send in submissions for the end of every show.
He did have a song with the verse:
You're a real good buddy of mine
And this was perhaps part of the same song, or a different one:
Great day in the morning
Everything's all right
[. . .]
Now, I don't care if the sun don't shine
We're gonna have us a real good time
Whether sunshine or pouring rain
The bottom line is still the same
I had almost convinced myself it was an elaborate dream until I saw this post. I also believe it might have been PBS, since I sort of associate it with seeing The Big Comfy Couch (which I know was on WUSF in St. Petersburg, FL), but I've scoured Wikipedia to no avail.