Yes your wife can apply a Filipino passport for your son.
If your son used his british passport on arrival in Phils together with his mum then he will automatically get stamp of 1yr stay free but to make sure bring his birth certificate and your Marriage Certificate incase the immigration officer ask for evidence.
i'm thinking it might just be safer to get him both passports and dual nationality anyway....[/QUOTE]
Having dual nationatily, he can get all the benefits he could be entitled either in UK or Phils.
Hope this helps.