Is there a way to save a X = 0 Stonecoil Serpent?
Yes, you can save the Serpent, but it must be set up ahead of time. There are two main ways of saving it that I can think of.

An anthem effect (called a static ability), like the namesake Glorious Anthem
Another card that says it enters the battlefield with +1/+1 counters on it (called a replacement effect), like Bloodspore Thrinax

Either of these will make sure the Serpent has toughness greater than 0 by the time state-based actions are checked. Note that this (in particular point 2) is in contrast to triggered abilities (like The Great Henge), which are too late to save the serpent.