Devotion is continuously kept up to date based on the current board state. It will be kept up to date between two spells on the stack resolving. (I wouldn't even call that "instant speed", which is more appropriate for describing things that go on the stack. You just keep it up to date continuously.)
The Devotion ability of gods —
As long as your devotion to {color/s} is less than {five/seven}, ~ isn't a creature.
— is a static ability that creates a continuous effect, and as the rules on continuous effects say:
611.3. A continuous effect may be generated by the static ability of an object.
611.3a A continuous effect generated by a static ability isn’t “locked in”; it applies at any given moment to whatever its text indicates.
The very moment a permanent that contributes to devotion enters or leaves your battlefield, your devotion is changed, and your gods on the battlefield1 may become creatures or cease to be creatures.
This means that if a spell or ability that says "target creature" is cast targeting only Keranos, and someone pulls this maneuver to de-creature-ify him, he will almost certainly not be a valid target at resolution time and the spell will fizzle. The same goes for other gods.
Your scenario itself is a little more complex. Suspension Field is not an instant or sorcery; it's an enchantment with an enters-the-battlefield ability. You don't choose targets while Suspension Field is on the stack — you just let it resolve. Then its ability triggers, and you choose targets for that. This maneuver would cause that ability to fizzle, then the Suspension Field would be left sitting uselessly on the battlefield.
For instants and sorceries though: an instant or sorcery like Burn from Within would lose its only valid target and fizzle. However Radiant Purge would still resolve fully and exile Keranos, because he still meets the targeting criteria (he's a multicolored enchantment).
1: Since this static ability is not a characteristic defining ability, it only functions on the battlefield. Gods who aren't on the battlefield are always legendary enchantment creatures.