Multiple instances of silvery barbs can affect the same roll
I assume that when you say "it passes the save", you're referring to the reroll – that is, the creature successfully made a saving throw against some other effect, and then the reroll forced by the first silvery barbs spell is still not sufficient to make them fail the saving throw, and now the second wizard wants to cast silvery barbs to create a second reroll and possibly make them fail.
Here is the rule for Combining Magical Effects (PHB, p. 204) that you refer to when you mention spell effects not stacking:
The effects of different spells add together while the durations of those spells overlap. The effects of the same spell cast multiple times don't combine, however. Instead, the most potent effect—such as the highest bonus—from those castings applies while their durations overlap, or the most recent effect applies if the castings are equally potent and their durations overlap.
The duration of silvery barbs is instantaneous – that is, the spell does not create an ongoing effect – so there are no durations that could overlap to make the rule apply.
Consider two casters casting fireball on the same creature (let's say, one with a readied action to the other casting): you also would apply the damage from both, not only from the one that has the higher result, because they resolve in an instant.