We consider a class of suspensions of diffeomorphisms of the annulus as flows in the orientable 3-manifold T$^2$ x I. Using results of Birman & Williams (Topology 22, 47-82 (1983); Contemp. Math. 20, 1-60 (1983)), we construct a knotholder or template that carries the set of periodic orbits of the flow. We define rotation numbers and show that any orbit of period q and rotation number p/q can be arranged as a positive braid on p strands. This yields existence and uniqueness results for families of resonant torus knots (p-braids that are (p, q)-torus knots of period q > p), which correspond to order-preserving (Birkhoff-) periodic orbits of the diffeomorphism. We show that all other q-periodic p-braids have higher genus, and we establish bounds on the genera of such knots. We obtain existence and uniqueness results for a number of other, non-resonant, torus knots, including non-order-preserving (q+s, q)-torus knots of rotation number 1.