Sir,
I had a Baby 6 month before in USA. We are Indian Citizen working in USA with L1 visa. My wife is home maker. Are we eligible to stay in USA for US Citizen child for the good quality education and life ? Can we apply for Green Card ?

Not based on having a USC child.

But if you are an L-1A, your company can file permanent residence for you as an international executive EB-1(3). You can file the AOS concurrently with the I-140 and your wife can be included on the petition. Check with your HR and the company immigration counsel. Good luck.