We have studied the evolution of magnetic and orbital excitations as a function of hole doping in single-crystal samples of Sr2Ir1 -xRhxO4 (0.07 ≤x ≤0.42 ) using high-resolution Ir L3-edge resonant inelastic x-ray scattering. Within the antiferromagnetically ordered region of the phase diagram (x ≤0.17 ) we observe highly dispersive magnon and spin-orbit exciton modes. Interestingly, both the magnon gap energy and the magnon bandwidth appear to increase as a function of doping, resulting in a hardening of the magnon mode with increasing hole doping. As a result, the observed spin dynamics of hole-doped iridates more closely resemble those of the electron-doped, rather than hole-doped, cuprates. Within the paramagnetic region of the phase diagram (0.17 ≤x ≤0.42 ) the low-lying magnon mode disappears, and we find no evidence of spin fluctuations in this regime. In addition, we observe that the orbital excitations become essentially dispersionless in the paramagnetic phase, indicating that magnetic order plays a crucial role in the propagation of the spin-orbit exciton.