If I am an student on an F1 visa and my wife is on an F2 visa, what are our chances of getting to be permanent residents since our son was born in the US?
You have no basis to just become permanent residents because you are students.  You have to be petitioned for permanent residence, either by a US employer on the basis of a valid fulltime offer of employment or a by a qualifying family relative.  Your son born in the US is such a relative; however, your child has to reach the age of 21 before he can petition for your permanent residence.