Today, as several other comments have noted, cargo aircraft launching drone swarms are the most likely future development (along with further missile development). Cargo aircraft have vast capacity in both mass and volume. Drones which dispense with the need to support a human pilot, and can operate one-way / kamakazi mode (though return flight is an option), and often have limited top speeds and ranges, make far more sense than a lightweight (and typically limited-capability) manned fighter or bomber.
Another line of nontraditional aircraft carriers are those based on submarines, with the Japanese deploying several during WWII (these enacted the only Japanese aerial attacks on the US mainland, near Santa Barbara and along the Oregon coast), and I believe there was a Soviet study (possibly 941-BIS) to develop a large-scale submarine aircraft carrier. As with airborne aircraft carriers, submarine-as-missile-launch-platform (ballistic or cruise) is far more practicable.