But why the concern with tofu? Unless your child is allergic to it, it should be safe during times of cough. And it depends what is the cause of the cough. If it is asthmatic, food can also be triggers.
If no allergy to tofu and having cough, I would say avoid chicken and eggs.
I was told by my Sinseh, do not use IKAN Bilis, Soya product, Chicken, Egg and Fish or Seafood when cough. They will make you cough more. Maybe you want to take note.
My sinseh told me that my son can't take tofu when he has cough and phlegm, as he is the "liang" type. Chicken and egg also to be avoided. Egg do increase phlegm, as I gave elder gal when she has a cough. I can hear her phlegm increase, so I stopped giving her eggs for the time being. Like what Fion73 says, fish and seafood also needs to be avoided but it depends on individual. I gave my kids fish, and their cough didn't worsen. Hope this helps.