We report the results of a Dark Energy Camera optical follow-up of the gravitational-wave (GW) event GW151226, discovered by the Advanced Laser Interferometer Gravitational-wave Observatory detectors. Our observations cover 28.8 deg(2) of the localization region in the i and z bands (containing 3% of the BAYESTAR localization probability), starting 10 hr after the event was announced and spanning four epochs at 2-24 days after the GW detection. We achieve 5 sigma point-source limiting magnitudes of i approximate to 21.7 and z approximate to 21.5, with a scatter of 0.4 mag, in our difference images. Given the two-day delay, we search this area for a rapidly declining optical counterpart with greater than or similar to 3 sigma significance steady decline between the first and final observations. We recover four sources that pass our selection criteria, of which three are cataloged active galactic nuclei. The fourth source is offset by 5.8 arcsec from the center of a galaxy at a distance of 187 Mpc, exhibits a rapid decline by 0.5 mag over 4 days, and has a red color of i - z approximate to 0.3 mag. These properties could satisfy a set of cuts designed to identify kilonovae. However, this source was detected several times, starting 94 days prior to GW151226, in the Pan-STARRS Survey for Transients (dubbed as PS15cdi) and is therefore unrelated to the GW event. Given its long-term behavior, PS15cdi is likely a Type IIP supernova that transitioned out of its plateau phase during our observations, mimicking a kilonova-like behavior. We comment on the implications of this detection for contamination in future optical follow-up observations.