I perused (but did not read completely) The Billiard Encyclopedia (1st ed. ) and Hendricks' history, but did not see any mention of diamonds in either.
There is mention of rail spots at the upper end of the table in White's Practical Treatise (1807), but it is not clear that there are spots everywhere, like we have diamonds today.
Mingaud (1831, 2nd ed.) clearly does not show any diamonds.
Tillotson (1836) does not even show rails, so we might be safe to presume that there were no diamonds.
I don't have any other works until about 1880, by which time they are in the diagrams.
Mike Shamos has some history in his Illustrated Encyclopedia, under the entry for "diamond." He generally concurs with a date between 1850 and 1855.