The DRAGON recoil mass separator at TRIUMF exists to study radiative proton and alpha capture reactions, which are important in a variety of astrophysical scenarios. DRAGON experiments require a data acquisition system that can be triggered on either reaction product ($gamma$ ray or heavy ion), with the additional requirement of being able to promptly recognize coincidence events in an online environment. To this end, we have designed and implemented a new data acquisition system for DRAGON which consists of two independently triggered readouts. Events from both systems are recorded with timestamps from a $20$ MHz clock that are used to tag coincidences in the earliest possible stage of the data analysis. Here we report on the design, implementation, and commissioning of the new DRAGON data acquisition system, including the hardware, trigger logic, coincidence reconstruction algorithm, and live time considerations. We also discuss the results of an experiment commissioning the new system, which measured the strength of the $E_{text{c}.text{m}.} = 1113$ keV resonance in the $^{20}$Ne$left(p, gamma right)^{21}$Na radiative proton capture reaction.
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