We study the possibility of using CsINa scintillators as an advantageous target for the detection of coherent elastic neutrino-nucleus scattering (CENNS), using the neutrino emissions from the SNS spallation source at Oak Ridge National Laboratory. The response of this material to low-energy nuclear recoils like those expected from this process is characterized. Backgrounds are studied using a 2kg low-background prototype crystal in a dedicated radiation shield. The conclusion is that a planned 14kg detector should measure approximately 550 CENNS events per year above a demonstrated ~7keVnr low-energy threshold, with a signal-to-background ratio sufficient for a first measurement of the CENNS cross-section. The cross-section for the Pb208(νe,e−)Bi208 reaction, of interest for future supernova neutrino detection, can be simultaneously obtained.