Would you like to play tennis tomorrow afternoon?

Literal

Tomorrow [possessive-の] afternoon, tennis [object-を] do-not [question-か].

The polite negative-question invitation ~ませんか — literally 'won't you [do X]?' — is the standard way to invite politely. The negation softens the ask. テニスをする is the standard collocation for 'play tennis' (する rather than 遊ぶ).