If you came to the USA on a tourist B1/B2 visa, which is only good for 6 months and have remained in the US on "over stay" for the past 3 years, and you want to marry an American, can that person get a Green Card by marrying the American citizen? Is being on overstay Illegal? They did come to the USA LEGALLY. Are they then eligible for Citizenship after they get the Green card. They also have a minor child-what would his status be?

Yes, an overstay of an I-94 creates unlawful presence, rendering that person deportable.

The good news is that INA section 245(a) allows for spouse of a USC to adjust status. This section waives the inadmissibitly ground of overstay and unauthorized employment.

After LPR status granted, and if meets the othe requirements, can apply for citizenship.

Child is not material to the case other than to prove up the bona fides of the marriage. Good luck.