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

Sure.

Baby born when parents are 18.  In 36 years, the ratio is 54:36 = 3:2.
Baby born when parents are 19.  In 38 years, the ratio is 57:38 = 3:2
Baby born when parents are 20.  In 40 years, the ratio is 60:40 = 3:2
Baby born when parents are 21.  In 42 years, the ratio is 63:42 = 3:2
.
.
.
Baby born when parents are 30.  In 60 years, the ratio is 90:60 = 3:2
Baby born when parents are 31.  In 62 years, the ratio is 93:62 = 3:2
Baby born when parents are 32.  In 64 years, the ratio is 96:64 = 3:2
Baby born when parents are 33.  In 66 years, the ratio is 99:66 = 3:2

So there you have 16 possibilities that can give you the ratio of 3:2 ,
for parents having a child when they're 18 or older, and living to less
than 100.

I'm not sure exactly but my best guess would be 1/4