The earliest use "a slow day" I can find in Google Books is from an 1847 story in Fraser's Magazine called The Keeping-Room of an Inn; Or, A Long Night and a Long Story, written by Thomas Chandler Haliburton, a Canadian judge and author.:
... a- working as hard as you can turning one thumb over the other, is dull music. It makes a slow day of it, and this has been about the longest I ever passed ; though, after all, it ain't to be named with an endless night I once spent. It was longer than you, Broadeloth, who are only five feet nothin', ...
A similar phrase may have appeared in an 1841 American Turf Register and Sporting Magazine:
... now I've drinked good — we'll have a bite and rest a while, and smoke a pipe, and then we'll use them quail, and we'll have time to pick up twenty cock in Hell-hole arterwards, and that won't be a slow day's work, I reckon. ...
It's become a more common term since then, but then again, the same concept may have just as commonly been expressed earlier using other words and spellings.
For example, King John from Shakespeare's King John says:
Good friend, thou hast no cause to say so yet,
But thou shalt have; and creep time ne'er so slow,
Yet it shall come from me to do thee good.
The Player King from Hamlet says:
My spirits grow dull, and fain I would beguile
The tedious day with sleep.
And Juliet in Romeo and Juliet:
O, I have bought the mansion of a love,
But not possess'd it, and, though I am sold,
Not yet enjoy'd: so tedious is this day
As is the night before some festival
To an impatient child that hath new robes
And may not wear them. O, here comes my nurse,
And she brings news; and every tongue that speaks
But Romeo's name speaks heavenly eloquence.