This paper considers several integral representations for the axially symmetric Helmholtz Green's function. In addition to the usual physical and mathematical forms that have recently been considered in the literature, it is demonstrated that contour deformation schemes lead to rapidly convergent integrals, particularly in cases where the integrands of the standard forms are highly oscillatory. The various forms together provide an efficient computational scheme over a wide range of coordinates. One form, which does not appear to be widely known, involves exponentially convergent integrals, the integrands of which involve only elementary functions. Although the focus here is on the Helmholtz, or reduced wave, equation, the methods described may readily be adapted to the Green's functions of similar differential operators.