If your BIL has held a green card for at least 5 years and applied for citizenship, there is no need to write any "letter of recommendation" and you are wasting your time. It will not be considered.
If BIL is not a legal immigrant holding a valid green card, there's nothing you can do for him. Only a US citizen parent, sibling, spouse or adult child over 21 who earns enough to support him can petition for his immigration. If his immigration visa is approved, then he can enter the US and subsequently apply for a green card. Depending on his ciitzenship and relationship to his sponsor, it can take up to 23-24 years to obtain an immmigration visa and enter the US.
If BIL is an illegal alien, he has NO choice but to return to his country of citizenship. There is no way to legalize an illegal alien, not marriage, not procreation. If you attempt to do anything to "help" an illegal alien remain in the US in violation of law, you are subject to 10 years in prison plus $250,000 fine.
So what's really going on here? His child has a right to citizenship in its father's country of citizenship, so he can be a better father, a law-abiding role model for his child, in his own country & take his kid with him.
You cannot sponsor your brother in law for a greencard. His spouse can if the spouse is an US citizen.
A letter of yours recommending him for citizenship is a waste of time. If you want to help them, pay for an immigration lawyer for him, for I imagine there are some legal problems involved why you feel impelled to write a letter.