Magnetic domains are used to represent binary digits in magnetic memories. In domain-motion magnetic memories, the domain must move longitudinally along a ferromagnetic nanowire. Antiferromagnetically coupled magnetic skyrmions, which are domains meeting this requirement, can be stabilized via the Dzyaloshinskii-Moriya interaction (DMI) in an antiferromagnetically coupled bi-layered perpendicularly magnetized thin wire. We find that antiferromagnetically coupled skyrmion-like bubble domains (BDs) may be produced in such a wire without DMI. The stability and the dynamics of such domains are studied by micromagnetic simulations based on the Landau-Lifshitz-Gilbert equation. The BDs in the two layers have clockwise and anti-clockwise Bloch type domain walls, so the BD cores have anti-parallel magnetic moments and are antiferromagnetically coupled. Domain size decreases with decreasing wire width and/or increasing antiferromagnetic coupling strength of the wire. The minimum value of the BD radius is about 10 nm. When a spin-polarized current flows through the wire, the BD moves with the current.