To my mind, the gold standard for this sort of analysis is FFG's Monster's Handbook. Using those guidelines, the first thing to do is to quantify the power of this ability -- if it were a spell, what level would it be? This is the trickiest part of the process, since assigning a level to a new spell usually comes down to some judgement calls.
This monster's ability is a really nasty, /permanent/ effect. The closest analogue I can think of is the 5th-level symbol of pain, which approxmates only only one application of bestow curse (-4 to rolls) on a temporary basis.
So let's say we start with base spell level of 5, add +2 levels to make the effect permanent, and another +1 level to reflect the multiple applications of the spell (-6 to one ability score, etc.) An 8th level spell? That looks about right, especially next to symbol of death.
Once we've got this down, the next step is to assign the new ability its own CR rating, just as if it were a separate monster. The Monster's Handbook suggests that adding a new spell-like ability that approximates an 8th-level spell is much like adding a second 12 CR monster to an encounter.
Although you call this a spell-like ability, your description of this as a song makes it sound more like a supernatural ability (which can't be disrupted). Making this spell-like ability a magical ability with 30 ft range would increase the CR by another +1, for a total CR of 13.
Adding this new CR 13 ability, then, to your original CR 12 demon is like setting up an encounter with 1 CR 12 monster and 1 CR 13 monster.
2 CR 12 creatures = EL 14; 1 CR 12 creature + 1 CR 14 creature = EL 15, so the adjusted CR for your monster would be somewhere between 14 and 15 (14.53, to be more precise).
Hope this helps!