What would the containment procedures say for an SCP that is an Alert System of unknown origin, therefore uncontainable?
That's pretty vague, but you could have audio dampeners or cancellers, teams set to keep information from going public, a public cover story if that isn't possible…
What kind of alert is it, or, how does it manifest?
Signal jammers could also work against things like radio or TV broadcasts.
For some examples of more unusual solutions that have been done before,
SCP-2206 involves a neighboring dimension's super-baseball radio coverage bleeding through at a huge number of places (presumably coinciding with broadcast towers in said alternate dimension). It would be really expensive and disruptive to jam full-strength broadcasts all over the place, so instead they've set up a whole franchise designed to convince people that it's a weird radio program, like some sort of really violent Wacky Races.
In the case of SCP-2049, (The Interdimensional Weather Station) they can't jam the signal because of the way it's broadcast, so they just debunk it and its effects as a hoax and focus on cleanup afterward.