Not really. Το παιδί σου translates to 'your child'. Σου declares possession in this case. ^.^
The child plays with you - Το παιδί παίζει μαζί σου/με εσένα
The child plays you (which doesn't make that much sense in English, but young children in Greece use the expression σε παίζουμε as in hanging out and play with you) - Το παιδί σε παίζει
Well, play with someone translates to παίζω μαζί με/με κάποιον in Greek.
Will you play with me? - Θα παίξεις μαζί μου;
I won't play with you - Δεν θα παίξω μαζί σου/με εσένα.
Εσένα (the accusative form of the pronoun εσύ) translates to you , and can be found in the tips and notes here https://www.duolingo.com/skill/el/Personal-objective-pronouns
In case you have any further questions or concerns about any of the above, feel free to ask. ^.^