A DM could rule however she chooses, but ruling that you can Sneak Attack with a Magic Stone fired from a sling is not against the rules:
"The attack must use a finesse or ranged weapon." (Basic Rules, p.27)
"You or someone else can make a ranged spell attack with one of the pebbles by throwing it or hurling it with a sling." (EEPC, p.20)
If you throw a Magic Stone pebble with a sling, you are making a ranged spell attack, but with a ranged weapon. Sneak Attack doesn't say it must be made with a weapon attack, it simply says the attack (melee, ranged, or spell) must use a finesse or ranged weapon. This is significant, because the type of attack (melee, ranged, or spell) does not have to match the means of delivering the attack -- for example, you can deliver a melee weapon attack with an unarmed strike, despite the unarmed strike not being a weapon.
Note, though, that the pebble isn't a weapon, so simply throwing the Magic Stone doesn't qualify you to use Sneak Attack, just as making a melee weapon attack with an unarmed strike (which isn't a weapon) doesn't allow you to add Sneak Attack to your unarmed strike damage. Getting to use Sneak Attack with a sling-delivered Magic Stone is simply the logical extension of not getting to use it with a monk's unarmed strike.
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Pauper