Femtosecond lasers are a proven source of hard X-rays for ultrafast probing applications; however, such X-ray sources do not offer significant advantages over accelerator-based photon sources. In this paper, the use of the proposed 100-kHz two-cycle ALPS-HR laser at the ELI-ALPS facility to drive a femtosecond hard X-ray source is investigated and target-related issues for high repetition rates are also discussed. A particle-in-cell simulation is used to determine the optimal plasma scale length for the investigated laser parameters to generate the necessary hot electron spectrum. Electron transport and photon creation are simulated using a Monte Carlo method in liquid droplet targets. The generated photon characteristics are postprocessed to build the synthetic X-ray spectrum and temporal pulse shape. The X-ray source characteristics are compared with other similar laser plasma X-ray sources. The parameters for the preliminary experiments are also discussed.