This is an old poem - I don't know of any tune for it. I found it in a c.1920 needlework journal, where it was referred to as being from the previous century.

A Stocking In Rhyme

To knit a stocking, needles four;
Cast on three needles and no more;
Each needle stitches eight-and-twenty,
Then one for seam-stitch will be plenty.
For twenty rounds your stitch must be
Two plain, two purl alternately.
Except the seam-stitch, which you do
Once purl, once plain the whole way through.
A finger plain you next must knit
Ere you begin to narrow it;
But if you like the stocking long
Two fingers length will not be wrong.
And then the narrowings to make,
Two stitches you together take
Each side the seam; then eight rounds plain
Before you narrow it again.
Ten narrowings you'll surely find
Will shape the stocking to your mind;
Then twenty rounds knit plain must be,
And stitches sixty-five you'll see.
Theses just in half you must divide,
With thirty-two on either side.
But on one needle there must be,
Seam-stitch in middle, thirty-three.
One half on needles two you place
And leave alone a little space;
The others, with the seam in middle,
To manage right is now my riddle.
Backward and forward you must knit,
And always purl the backward bit;
But seam-stitch purl and plain, you know,
And slip the first stitch every row.
When thirty rows you thus have done,
Each side the seam knit two in one
Each third row until sure you feel
That forty rows are in your heel.
You then begin the heel to close;
For this choose one of the plain rows;
Knit plain to seam, then two in one,
One plain stitch more must still be done.
Then turn your work, purl as before
The seam stitch – two in one one more;
Then turn again, knit til you see
Where first you turned, a gap will be.
Across it knit together two,
And don't forget one plain to do;
Then turn again, purl as before,
And sew til there's a gap no more.
The seam stitch you no longer mind;
That, with the heel, is left behind.

When all the heel is quite closed in,
To knit a plain row you begin,
And at the end you turn no more,
But round and round knit as before.
When all the heel is quite closed in,
To knit a plain row you begin,
And at the end you turn no more,
But round and round knit as before.
For this, on a side needle take
The loops the first slip-stitches make;
With your heel needle – knit them plain,
To meet the old front half again.
This on one needle knit should be,
And then you'll have a needle free
To take up loops the other side,
And knit round plain, and to divide
The back heel parts evenly in two;
Off the heel needle some are due;
Be careful that you count the same,
On each back needle knit round plain;
But as the foot is much too wide,
Take two together at each side,
On the back needle where they meet
The front to make a seam quite neat.
Each time between knit one plain round,
Til stitches sixty-four are found;
And the front needle does not lack
As many as on both the back.
You next knit fifty-six rounds plain,
But do not narrow it again;
'Twill then be long enough, and so
Begin to narrow for the toe.
Your long front row knit plainly through,
But at its end knit stitches two
Together, and together catch
Two first in the next row to match;
Then to the other side knit plain
Half round, and do the same again;
That is, two last together catch,
Two first, in the front row to match.
At first knit four plain rounds between,
Then two, then one, until 'tis seen
You've knit enough to close the toe;
And then decrease in every row,
Until to stitches eight you're brought,
Then break the thread off – not too short –
And as these stitches eight you do,
Each time your end of thread pull through;
Then draw it up and close it tight,
And with a darning needle bright,
Your end of thread securely run,
And then, hurrah! The stocking's done!