Below are some quotes from academic works suggesting possible dates for P52.
“Any exact dating of book hands, is of course, out of the question; all we can do is compare the script as a whole and the forms of particular letters with those found in other texts and particularly in dated documents”
“The scribe writes in a heavy, rounded and rather elaborate hand, often uses several strokes to form a single letter with a rather clumsy effect and is fond of adding a small flourish or hook to the end of his strokes some of these features can be paralleled from dated documents”
Both the above excerpts are from Colin H. Roberts book. An Unpublished Fragment of the Fourth Gospel in the John Rylands Library. Manchester: the Manchester University Press, 1935. p. 13
“The manuscripts P46, P52, P87, P104 belong to a specific type of bureaucratic and chancery script. P52 can be compared with P. Fayum 87 (PARSONS–TURNER, 1987, pl. 48; TM 10930), written in 156 and one of the earliest dated."
Taken from A Critique of Theological Palaeography, Pasquale Orsini & Willy Clarysse as cited at http://vridar.org/2013/03/08/new-date-for-that-st-johns-fragment-rylands-library-papyrus-p52/