How would you write Light Yagami's name in the Death Note? I don't know Japanese script, but Light would be spelled "Tsuki" which means "moon". So which of "Tsuki" or "Raito" can kill him? Would "Light" in English work?

It seems the death note is a stickler for spelling, as shown here: What did Light write before killing Shibuimaru Takuo?
Remember that the Death Note is very specific about using the original spelling for a name.


  So which of "Tsuki" or "Raito" can kill him?


The only one that matters, 月 or "tsuki". Early in the manga he makes a point about the pronunciation for this very reason.


  Would "Light" in English work?


no. The original spelling is required.

The following will work:


夜神月


The following will not work:


夜神
月
ヤガミライト
Yagami Raito
Yagami Light
Light