The song is awfully close to Rockin' Alone (In An Old Rocking Chair) by Miki & Griff (with many covers by many others). You can listen to it here; my transcription of that link follows. It does lack the ending line.

ROCKIN' ALONE (IN AN OLD ROCKING CHAIR)
(Bob Miller)

Sitting alone in an old rocking chair
I saw an old mother with silvery hair
She seemed so neglected by those who should care
Rocking alone in an old rocking chair

It wouldn't take much just to gladden her heart
Just some small remembrance on somebody's part
A letter would brighten her lonely life then
Rocking alone in an old rocking chair

I know some youngsters in an orphan home
Who'd think they were in Heaven if she were their own
They'd never be willing to let her sit there
Rocking alone in an old rocking chair

I look at her and I think it a shame
The ones who've forgot her, she loves just the same
And I think of angels as I see her there
Rocking alone in an old rocking chair