This study considers two-degree-of-freedom planar tensegrity-inspired manipulators composed of anti-parallelogram (X) and revolute (R) joints containing springs and actuated remotely by four cables. The goal is to design the constituent elements of these manipulators while they carry a given payload in the presence of gravity. While this is a classical problem in serial and parallel manipulators with known approaches in the literature, their extension to tensegrity-inspired manipulators is challenging due to the presence of springs and actuation by cables. In this paper, we address all these challenges in a sequence for the 2-X and 2-R manipulators. Firstly, we discuss the limits on joint movement due to the geometry and spring free length. Then, we find the set of all feasible springs that can be installed on these joints while respecting their mechanical constraints, e.g., maximum elongation. We estimate the axial loads in the bars to obtain cross-sections safe from buckling failure. Finally, we compute the stable wrench-feasible joint space (SWFJ) and stable wrench-feasible workspace (SWFW) for the two manipulators. This study will serve as a basis for design optimization of the two manipulators.