What would be the best word for vulnerable?
just to give an example:
"His face was like that of a young and vulnerable child."
In the context you have given, you are using the nuance of guilelessness in reference to vulnerability. Indeed, mahina (weak) is a valid equivalent of vulnerable but it seems that is not what you are trying to convey given your sample text.
Instead it seems you wish to emphasize the nuance of childlike innocence when you use the word vulnerable. Thus, I would suggest
Mukha siyang bata at inosente OR
Mukha siyang batang inosente.
If you did mean to say vulnerable in the sense of helplessness ("he looks young and helpless") then you could use
walang kalaban-laban (
Mukha siyang batang walang kalaban-laban).