We present the discovery of variable stars in two isolated dwarf galaxies in the outskirts of the Local Group, VV 124 and KKr 25, using observations with the Hubble Space Telescope. VV 124 hosts stellar populations with a wide range of ages (>10 Gyr until the present) and therefore we find all types of classical pulsators. In VV 124, we detect a total of 771 variable stars, including 78 classical Cepheids, 10 anomalous Cepheids, one Type II Cepheid, 678 RR Lyrae stars, and four eclipsing binaries. In KKr 25, we find 25 anomalous Cepheids, 46 RR Lyrae stars, and no classical Cepheids, thus the galaxy does not have a strong young population. A comparison of the variables with evolutionary tracks suggests that both galaxies may contain an intrinsic spread in metallicity, but overall are fairly metal-poor. We also present detailed simulations, which have been designed to estimate the completeness of our variable catalog. Particularly in the cases for which the observations are not deep enough to reach the main-sequence turnoff, such as the more distant Local Group dwarf galaxies, the techniques developed here can be used together with relatively shallow color-magnitude diagrams to inform on the nature of galactic populations over the full range of ages.