Can a ratio of a parents age to his or her child's age ever be exactly 3: 2?

Of course !

-- Child born when parents are 18.
    Child is 36 when parents are 54.

-- Child born when the parents are 21.
   Child is 42 when parents are 63.

-- Child born when parents are 24.
   Child is 48 when parents are 72.

-- Child born when parents are 27.
   Child is 54 when parents are 81.

-- Child born when parents are 30.
   Child is 60 when parents are 90.

Stretching it:
-- Child born when parents are 33.
   Child is 66 when parents are 99.