Can "childs" ever be the plural of "child", in standard English?

Solution 1:

No, "childs" was never a plural of child. See Etymononline's entry for child:

The difficulty with the plural began in Old English, where the nominative plural was at first cild, identical with the singular, then c.975 a plural form cildru (genitive cildra) arose, probably for clarity's sake, only to be re-pluraled late 12c. as children, which is thus a double plural. Middle English plural cildre survives in Lancashire dialect childer and in Childermas.

The German equivalent of children is Kinder, the Dutch kinderen. The plural form with r in children seems very stable. So it is improbable that children will ever be replaced with childs.

Solution 2:

The word in Old English is the neuter noun cild, which wasn't inflected for nominative and accusative, either singular or plural. (You can check out the Old English Translator if you wish.) In late Old English, the word took on the inflections of another class of neuter nouns, those with -u/-o stems, which had nominative plurals -ru. This per the OED. (You can also go here.) Thus the plural (in the nominative) became cildru. This change was adopted in the southern dialects, but the north was more conservative, with Northumbrian keeping cild and making its plural cildas, from an attraction to that plural of -a stem masculine nouns. Further north in Scotland, there is the Scottish chield, which always had the plural chields.

Middle English moved the -ru ending to -re, which eventually became the standard for dialects, north and south. The north retained the plural childre, but the south adopted children as the plural along the lines of other nouns ending in -re like brethre (brother) with its plural brethren.

The OED tells us that childes survived until the 15th century from the Northumbrian cildas, but that children became the "standard and literary" winner.