Corals take up inorganic carbon (as CO2 itself or bicarbonate as the source of the CO2) and typically are net producers of DOC when healthy, although not always. If bleached they can become net users of DOC, and they can in other situations as well.
To use DOC levels in a Redfield ratio of carbon to N and P nutrients to suggest the uptake needs for corals use is not seemingly appropriate since most of their carbon comes from other sources.
Can heterotrophic uptake of dissolved organic carbon and zooplankton mitigate carbon budget deficits in annually bleached corals?
https://aquaticbiogeochem.osu.edu/sites/aquaticbiogeochem.osu.edu/files/Levas et al (2016) Coral Reefs.pdf
Throughout the study, non-bleached control P. astreoides and O. faveolata released DOC (Fig. 4f, i), consistent with findings from most previous studies of healthy nonbleached coral DOC fluxes (Crossland 1987; Wild et al. 2004, 2005, 2008, 2010a, b; Tanaka et al. 2008, 2009; Haas et al. 2010; Naumann et al. 2010; Levas et al. 2015). At the same time, non-bleached control P. divaricata took up DOC after the single bleaching event (Fig. 4c), just as did healthy Pocillopora sp., Fungia sp., and Stylophora pistillata (Naumann et al. 2010; Tremblay et al. 2012). However, similar to P. astreoides and O. faveolata, nonbleached control P. divaricata released DOC during the remainder of the study (Fig. 4c). These findings further show that while DOC typically represents a loss of C from healthy corals, it can sometimes also be a source of C.