I just found this thread searching on Google for the same information...then I remembered where I'd found it before. If I may offer more fuel to the grandpaternal fire...

http://php.indiana.edu/~jbmorris/LYRICS/grandpa

According to this, Lonzo and Oscar wrote it, Jaffe and Latham composed it, and Lombardo, Harris, Jo Stafford, Homer & Jethro, and Ray Stevens all recorded versions of it (Stafford, of course, being her own grandma).

Hope this helps.