You can apply on line for a renewal - but I am wondering if your grandson is a minor, someone has to give parental consent but if you have legal guardian ship, I would have thought that you could do that.
I'm not aware that a birth certificate is required for a renewal but perhaps because of his age it is.
Even so I cannot see that the demise of his mother would make a difference, birth certificates are a statement of facts at birth, they don't get updated to reflect the passing of ones parents.
If this question relates to the need for a parental signature on a child's passport application, you can sign instead of either of your grandson's parents. Simply indicate your relationship as 'Grandparent/Guardian'.