Solid-state ionization chambers are presented based on thin diamond crystals that allow pulse-resolved intensity measurements at a hard X-ray free-electron laser (FEL), up to the 4.5 MHz repetition rate that will become available at the European XFEL. Due to the small X-ray absorption of diamond the thin detectors are semi-transparent which eases their use as non-invasive monitoring devices in the beam. FELs are characterized by strong pulse-to-pulse intensity fluctuations due to the self-amplified spontaneous emission (SASE) process and in many experiments it is mandatory to monitor the intensity of each individual pulse. Two diamond detectors with different electrode materials, beryllium and graphite, were tested as intensity monitors at the XCS endstation of the Linac Coherent Light Source (LCLS) using the pink SASE beam at 9 keV. The performance is compared with LCLS standard monitors that detect X-rays backscattered from thin SiN foils placed in the beam. The graphite detector can also be used as a beam position monitor although with rather coarse resolution.