Verified Answer :

MissLittlepurr

I know you said 2 numbers but here is a list :)
62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88

Two composite numbers between 60 and 90 are 67 and 79.   
Hoped I helped =)

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