The main disadvantages of BrahMos are
Only 120 km range when using Lo-altitude sea-skimming profile
Not intelligent ( can’t take evasive measures on its own to avoid interceptor missiles and follows predetermined path)
So basically the Onyx/Brahmos can be shot down using
LONG RANGE SAM:
The US Navy uses the SM-2 as its standard long range SAM on its destroyers. It has a range of 90+ km and uses a semi-active homing radar seeker which means that the mechanically scanning illuminators on board the warships should provide them with guidance.
MEDIUM RANGE SAM:
Once the missiles are detected by the AWACS at 150+ km from the ship, the usual procedure would be to direct fighter jets from a nearby carrier towards the missile to shoot it down. The 50 km range Evolved Sea Sparrow Missile (ESSM) which is quad packed and hence large quantities are available. This is very useful as one cell packs 4 MR-SAM compared to 1 LR-SAM.
SHORT RANGE (POINT DEFENSE) SAM:
This is a relatively simple task for systems like the Rolling Airframe Missile (RAM) or Barak-1 which are designed to kill sea skimming supersonic missiles.
The Phalanx CIWS is a closed loop system, with the search-tracking radar and the 20 mm Gatling gun and ammunition combined into a self-sustained system. It has a max range of 3 km and an effective range of 1.5 km when dealing with low flying cruise missiles. If it faces a single BrahMos which has bypassed other missile defense layers, the radar of the Phalanx locks on to the BrahMos and unleashes a torrent of 20 mm depleted uranium projectiles which should shred the BrahMos easily.
It is currently capable of shooting down slow aerial and surface targets, but with improvements, by the next decade, a laser CIWS would be widely deployed and would be capable of swatting multiple BrahMos missiles like flies.