It's unlikely that "stint" is related to German "Stund". The English cognate of "Stund" is the now archaic word "stound".
"Stint" comes from an Old English verb meaning "to blunten" (and possibly also meaning "to shorten"). The OED comments:
The Old English verb corresponds formally to Old Scandinavian *stynta (Middle Swedish stynta , Old Icelandic stytta ) to shorten ... It is uncertain whether the Middle English and modern English senses of the verb are developed from unrecorded senses in Old English, or are due to Scandinavian influence.
"Stint" in Middle English meant "to cut short, cease, stop".
From this the noun "stint", originally meaning "cessation of action, pause" (OED) developed. Later it came to mean "an allotted amount or measure", "an allotted portion of work", etc.