NGC 6819 is an open cluster of age 2.4 Gyr that was in the NASA Kepler spacecraft’s field of view from 2009 to 2013. The central part of the cluster was observed in a 200 × 200 pixel “superstamp” during these four years in 30 minute cadence photometry, providing a unique, high-precision, long time-series data set. The cluster contains “blue straggler” stars, i.e., stars on the main sequence above the cluster turnoff that should have left the main sequence to become red giants. We present light curves and pulsation frequency analyses derived from custom photometric reductions for five confirmed cluster members—four blue stragglers and one star near the main-sequence turnoff. Two of these stars show a rich spectrum of δ Scuti pulsation modes, with 236 and 124 significant frequencies identified, respectively, while two stars show mainly low-frequency modes, characteristic of γ Doradus variable stars. The fifth star, a known active X-ray binary, shows only several harmonics of two main frequencies. For the two δ Scuti stars, we use a frequency separation–mean density relation to estimate their mean densities, and then use these values along with their effective temperature to derive their stellar masses and radii. For the two stars showing low frequencies, we searched for period-spacing sequences that may be representative of gravity-mode or Rossby-mode sequences, but found no clear sequences. The common age for the cluster members, considered along with the frequencies, will provide valuable constraints for asteroseismic analyses, and may shed light on the origin of the blue stragglers.