We systematically investigate the microdomain morphologies that self-assemble in a diblock copolymer melt confined to a narrow cylindrical nanopore using real-space self-consistent mean-field theory. We observe, for a bulk cylinder-forming copolymer, that a variety of novel microdomain structures emerge under confinement. As the pore diameter increases, the following sequence of stable structures occurs: single cylinder, stacked disks, single helix, double helix, toroid-sphere, and helix-cylinder. We accurately locate the pore diameters where first-order phase transitions between these morphologies occur. We vary the interaction of the diblock copolymer with the pore wall from being preferential for the minority block to neutral to being preferential for the majority block and find that the sequence of structures is unchanged, for these interactions. The pitch angle of the helices and the pore diameter can be related using a simple geometrical argument. Over the range of pore diameters we examine, phases involving arrangements of multiple straight cylinders along the pore axis have significantly higher free energy than the structures mentioned above. Our results are consistent with experiments and a recent simulated annealing study.