I may soon encounter a situation where player characters might sneak up on some sleeping giants and try to murder them or steal their coins, which are stored in bags near the sleeping giants.

Sneaking up on the giants is clear: Sleeping character gets +10 DC on perception checks. Coup de grace is clear, though a risky proposition against a giant.

Suppose, then, that the characters do successfully sneak to the sleeping giants and coup de grace one or several of them. What is the DC for the others to wake up, supposing the attacked giants are slain? Battle is DC -10, details of a conversation are 0, so presumably -5 would be okay, unless the weapon is terribly noisy (a gun, say, or a morningstar).

If the other giants do wake up, how quickly can they act? Should I have everyone roll initiative and go with that, or give automatic surprise to the player characters, or something else?

The other likely action PCs might take is to steal some coins from the giants. They have several thousands in total, so stealing all of that is out of question. How would one check if this makes enough noise to wake a giant up? I think this should be related to the number of coins one steals and how quickly one does it. Sleight of hand and stealth are likely the relevant skills here.