A person that is ready for bedtime, often the sleepy person's friends are begging them to keep the party rolling.
James: I'm ready for bed. It's one in the morning.
Fred: Stop being a sleepy peepy and come dance!
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An unfortunately-timed flaccid penis.
Angela-- You had sleepy peepy again last night, Brendan. No more whiskey before bed.
Brendan-- : (
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peepies = eyes
so if you have sleepy peepies, then you have tired eyes
jasmine: I have had such a long day
Joanne: you look tired, you have sleepy peepies