Can I extend my stay in Thailand for 1-2 months if my work permit is not renewed?

Hes said his wife is NON thai and due to have baby.

As you're on an Extension of Stay based on work, this will end once you stop work and your WP is cancelled. You will have 7 days to leave. You should be able to change the reason for your extension to marriage, assuming you're married to a Thai and meet the financial conditions. As Billy Brown says, go and talk to your local Immigration office.

First, you are not on an extension based on your work permit. You should have a type B visa extension, which does expire when you no longer have your job.

Besides all that, here is the most important detail you didn't mention concerning your situation, and it is very relevant to how you can stay. Is your wife Thai, and if so are you legally married to her, having gotten married at the local Amphur, and not just some ceremony with the monks. If she is Thai, and you are legally married to her, then you can apply for a type O visa extension based on Thai Wife. Just take your two marriage documents, and your wife to immigration and apply. You should get a 90 day type O visa extension giving you time to meet all the other requirements to apply for your one year extension. Whether you apply for that, or not, is incidental as you do not plan on staying past 90 days, but if you do, you need to put at least bt400,000 in your bank account that is in your name only right away, then the rest is easy, as it is just collecting the documents needed. That is your best route to go, as long as your wife is Thai, and you are legally married.

Also, you can work when you have a type O visa extension based on Thai Wife, so you can apply for it right away.