"Give The World A Smile" is the answer. The Stamps recorded it a long time ago, a couple generations before J.D. and the boys' tenure.
The Blackwood Brothers recorded it as well. Here's a clip of a recording from them.
And here are the lyrics (not sure who penned them)--Elvis is heard singing the chorus:
Are you giving to the world a smile (sunny smile)
Helping lessen someone's dreary mile (dreary mile)
Do you greet the world with song as through life you pass along
Cheering those you may meet along life's way
Give the world a smile each day (give the world a bright smile every day)
Helping someone on life's way (helping someone on life's dreary way)
From the paths of sin (paths of sin) oh bring the wonderer's in (bring them in)
To the master's fold to stay (to His fold, His forever to stay)
Help to cheer the lone and sad (help cheer the sad, the lonely and sad)
Help to make some pilgrim glad (help make pilgrim, make somebody glad)
Let your life so be that (life so be that) all the world might see
The joy of serving Jesus with a smile (a bright sunny smile)
Give the world a happy song today (song today)
That will help some pilgrim on His way (on His way)
You can tell him of the Lord and His heavenly reward
If you'll only follow Jesus day by day
I'd never heard of the song before...I actually just figured this out.