I can't give quite as much information about this one as I'd like - there appears to be no good online source for the particular version of the song in question with which I'm familiar. However:

"Lady Howard's Coach" looks as if it should certainly qualify as traditional. The source of the verse is Sabine Baring-Gould, although from what I can find online I'm not certain which of several possible volumes is the most correct reference (possibilities include Songs of the West (1891 or 1905) and A Book of the West (1899). Dartmoor Resource has a Web page with a good deal of useful information, including a full set of lyrics as reconstructed by Baring-Gould.

Now, the version I know is a significantly streamlined text adapted by Pacific Northwest singer Cecilia Eng, for which I can find no good audio or video performance online (though it does exist on her album, Of Shoes and Ships). Here are lyrics for that version:

LADY HOWARD'S COACH (1)

words: Sabine Baring-Gould (v.1-2,5-6) & Cecilia Eng (v. 3-4)
music: Cecilia Eng © 1987


“Now pray step in,” my lady saith,
“Now pray step in and ride.”
I thank thee, I would rather walk
Than gather to thy side.

The wheels go round without a sound
Or tramp or turn of wheels.
As cloud at night, in pale moonlight
Along the carriage steals.

All black the coach my lady rides
And black the horses four,
And black the hound which makes no sound
But races on before.

My lady’s fair and dark of hair
And beckons me to ride.
Delights divine shall all be mine
If I should step inside.

I’d rather walk a hundred miles
And run by night and day
Than have that carriage halt for me
And hear my lady say:

“Now pray step in, and make no din,
Step in with me to ride;
There’s room, I trow, by me for you
And all the world beside.”

///

I know there's at least one completely different setting of this online somewhere, but that link has utterly vanished from my search streams.