Might I ask how? Its a second eldritch blast per turn with a 1/4 of its range and using your bonus action, and spending two invocations to do so at level 12. Doing 120 damage with a charisma of 20 if all attacks hit for max damage.
If you are able to perform eldritch blast twice every round, then this is essentially using the Fighter's Action Surge ability every round. The limited range is not enough to make up for this.

Erm... I'm not sure it can be balanced. It is basically an extra turn each round.

These weapons can be used as an arcane focus, and spells can be “shot” out of them.
I think that you should define what this means. Does the range of the spell change? Does the 'spell' hit like a normal ranged weapon attack? If so, does the creature get another saving throw against, say, charm person? Does the attack do normal damage as well? What if I sling a spell that has a target of 'self' (some spells are not supposed to be shared)? Has multiple targets? Has an area effect?

Quick shot(requires level 5): When you cast a cantrip you can make an attack with one of your Eldritch Slingers as a bonus action.
Say you cast Eldritch Blast, then you use your slinger to 'sling' a 4th level spell at the target. You basically perform a full-round damage attack (since EB scales with level), then get to cast a spell (?). This is more powerful than the 18th level Eldritch Knight feature.

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I think that the main concern here is that Eldritch Blast scales with level. At 11th level, a basic full-round attack for various classes is:
-Warlock: Eldritch Blast (3 rays)
-Fighter: 3 Attacks
-Paladin: 2 Attacks + Improved Divine Smite (+1d8 on each attack)
-Rogue: 1 Attack + Possibility of Sneak Attack (6d6)

They are all balanced around each other. Which means that if you get to do EB and another thing on your turn, you are breaking out of the normal paradigm greatly.