Past
Miroku's childhood is never really explored in depth. We do however know some things. Miroku's mother was never mentioned, one would assume that Miroku's father used the same tactics Miroku now uses to get a woman. That is to say told them the story of the kazaana then asked her to bear his child. Miroku never met his grandfather who was given the curse but knows of him.Miroku's birth date is never mentioned there's also really no indication as to the season or even the place he was born. As 19 seems to be the generally accepted age for Miroku almost the only thing we know about when Miroku's birth is is that it was 19 years ago. What happened to his mother is unknown, I tend to think she died in childbirth or something because we know that when Miroku's father is swallowed by the air rip he has been left in the care of a nearby temple.
As was previously mentioned, when Miroku's father was swallowed by his wind rip he was left in the care on Mushin, a corrupted old monk. Miroku appeared very young when his father died I'd say from about 6-8 years of age.
What happened to Miroku in the temple leading up to his quest to find Naraku is also a mystery. One can assume he completed his training as a monk during this time and began questing for Naraku however nothing concrete is really given except for a few tasks he completed, such as meeting Koharu when he was around the age of 16 (16 because he met Koharu when she was 11 and re-met him 3 years later as Koharu is 14, if the generally accepted age for Miroku of 19 stands he would have been 16 when he met Koharu for the first time.)