Fjold, of Calguns, brought up that the 22LR projectile is actually slightly smaller in diameter than a 223 projectile. This means that, while it will fire more or less reliably from an AR-15 barrel, there will be a degree of "slop" involved, which will greatly reduce the accuracy found by using a Ceiner or other conversion kit and a standard AR-15 barrel. It is recommended, if accuracy is even remotely of concern, to use a dedicated upper instead of a conversion kit.
CDNN offers the V-22 upper for $260. STRONGLY recommended in CA - it cannot be readily removed from the weapon once installed, and doesn't permit the installation of standard AR mags.
Bushmaster has a 22LR upper out for around $380 (seen online)