Looks like it's short for "you ones":

Yinz is the most recent derivation from the original Scots-Irish form you ones or "yous ones", a form of the second person plural commonly heard in parts of Ulster. When standard-English speakers talk in the first person or third person, they use different pronouns to distinguish between singular and plural. In the first person, for example, speakers use the singular I and the plural we. But when speaking in the second person, you performs double duty as both the singular form and the plural form. Crozier (1984) suggests that during the 19th century, when many Irish speakers switched to speaking English, they filled this gap with you ones, primarily because Irish has a singular second-person pronoun, tú, as well as a plural form, sibh. The following, therefore, is the most likely path from you ones to yinz: you ones [juː wʌnz] > you'uns [juːʌnz] > youns [juːnz] > yunz [jʌnz] > yinz [jɪ̈nz]. Because there are still speakers who use each form,[2] there is no stable second-person plural pronoun form in southwest or central Pennsylvania, which is why the pronoun is variably referred to or spelled as you'uns, y'ins, y'uns, yunz, yuns, yinz, yenz, yins or ynz.