The growth of single-walled bimetallic Au-Ag, Au-Cu and Ag-Cu alloy nanotubes (NTs) and nanowires (NWs) in confined carbon nanotubes (CNTs) has been investigated by using the classical molecular dynamics (MD) method. It is found that three kinds of single-walled gold-silver, gold-copper and silver-copper alloy NTs could indeed be formed in confined CNTs at any alloy concentration, whose geometric structures are less sensitive to the alloy concentration. And an extra nearly pure Au (Cu) chain will exist at the center of Au-Ag (Au-Cu and Ag-Cu) NTs when the diameters of the outside CNTs are big enough, thus producing a new type of tube-like alloy NWs. The bonding energy differences between the mono- and hetero-elements of the coinage metal atoms and the quasi-one-dimensional confinement from the CNT play important roles in suppressing effectively the "self-purification" effects, leading to formation of these coinage alloy NTs. In addition, the fluid-solid phase transition temperatures of the bimetallic alloy NTs are found to locate between those of the corresponding pure metal tubes. Finally, the dependences of the radial breathing mode (RBM) frequencies and the tube diameters of the alloy NTs on the alloying concentration were obtained, which will be very helpful for identifying both the alloying concentration and the alloy tube diameters in future experiments.