Not the oldest version, but close. My Blue Heaven, Jimmie Tarleton, 1930. Jimmie and Tom Darby were musical partners in a recording career that lasted from 1927 through 1933, but their relationship was sometimes a bit rocky. In the notes for Darby & Tarleton, Complete Recordings, Bear Family BCD 15764, Ed Kahn says:

My Blue Heaven was written by Walter Donaldson (music) and George Whiting (lyrics) in 1927 and became an instant hit by Gene Austin. Like so many songs, it found its way into folk tradition. Jimmie knew that the song was a Gene Austin hit and immediately incorporated it into his repertoire. It became somewhat of a showcase number for him. He kept it in his repertoire until the end of his life and stunned audiences in the 1960s with his rendition of this classic. Throughout his life he altered and modified the words to the song. The text he recorded in 1930 is quite different from the original hit.

Whatever the tensions between Darby and Tarlton, on December 3, 1930, Jimmie recorded six numbers in Atlanta without Tom. Jimmie indicated that the last session for Columbia was run by Bob Miller. Bob Miller said of Jimmie that he had "...the sweetest voice... " he had ever heard. He also indicated some disagreements between "...these boys and Columbia because they felt the recording company was trying to short-change them on their royalties, so Columbia let them go. "

My Blue Heaven
Walter Donaldson, music and George Whiting, lyrics, 1927
recorded by Jimmie Tarleton, December 3, 1930, with lyrics adapted by him

When whippoorwill calls and evening is nigh
I'll hurry to my little - (steel guitar notes instead of words)
She will turn to the right and I will cut out the light
Then me and her go back to my little - (steel guitar notes)
Just daddy and me and mama makes three
We'll both be so happy in my - (steel guitar notes)

A smiling face, a fireplace, a cosy room
A little nest, ah that nestles where my daddy rooms
Just mama and me and sweet daddy makes three
We'll both be so happy in my - (steel guitar notes)

Mama'll feel so bad and daddy'll be so glad
It'll be the best little blue heaven that you've ever - (steel guitar notes)
Just mama and me and sweet daddy makes three
We'll all be together up in my little - (steel guitar notes)

Says mama, "Don't you cry, but sweet daddy's 'bout to die
He'll still make things right up in your - (steel guitar notes)"
Just the angels and me, and Jesus makes three
He'll take us all home to my - (steel guitar notes)

Just mama and me, and sweet Jesus makes three
He'll make things so happy up in my blue heaven

I know I have heard the Gene Austin version, but if I have it, I have no idea where to find it. Maybe someone else has it buried away somewhere.

There is an RA clip of Blue Heaven from the CD Gene Austin, Voice of the Southland, ASV/Living Era 5217 at Venerable Music. The song also includes an introductory phrase, part of which you can hear on the clip which you can access from the linked page.

. . . love birds calling
What makes the world go round, nothing but love
When whippoorwills call, etc.

Read about Gene Austin (1900-1972) at Handbook of Texas Online Among other things, the site says that his recording of My Blue Heaven sold more than 12 million copies over the years.