A simple method for designing spatiotemporal coherency vortices (STCVs) and spatiotemporal dislocation curves (STDCs) is introduced by means of coherent-mode representation and Fourier transforms. A partially coherent pulsed beam is represented by an incoherent superposition of a Gaussian and a Hermite-Gaussian pulsed beam with different waist positions. It well demonstrates that there exist STCVs and STDCs in the space-time plane. The detailed numerical calculations are performed to address the dependence of waist distance of two modes, reference position, beam order, distribution of original spectrum, topological charge and mode weights ratio on the STCVs and STDCs. The physical interpretation behind numerical results is shown. A possible scheme for experimental synthesis of the STCVs is proposed. The obtained results may have potential applications in the fields of light-matter interaction, spatiotemporal spin-orbit angular momentum coupling and STCV-based optical trapping and optical manipulation.