The transfer of matter between a circumbinary disk and a young binary system remains poorly understood, obscuring the interpretation of accretion indicators. To explore the behavior of these indicators in multiple systems, we have performed the first systematic time-domain study of young binaries in the ultraviolet. We obtained far- and near-ultraviolet HST/COS spectra of the young spectroscopic binaries DQ Tau and UZ Tau E. Here we focus on the continuum from 2800 to 3200{AA} and on the CIV doublet ({lambda}{lambda}1548.19,1550.77{AA}) as accretion diagnostics. Each system was observed over three or four consecutive binary orbits, at phases ~0, 0.2, 0.5, and 0.7. Those observations are complemented by ground-based U-band measurements. Contrary to model predictions, we do not detect any clear correlation between accretion luminosity and phase. Further, we do not detect any correlation between CIV flux and phase. For both stars the appearance of the CIV line is similar to that of single Classical T Tauri Stars (CTTSs), despite the lack of stable long-lived circumstellar disks. However, unlike the case in single CTTSs, the narrow and broad components of the CIV lines are uncorrelated, and we argue that the narrow component is powered by processes other than accretion, such as flares in the stellar magnetospheres and/or enhanced activity in the upper atmosphere. We find that both stars contribute equally to the narrow component CIV flux in DQ Tau, but the primary dominates the narrow component CIV emission in UZ Tau E. The CIV broad component flux is correlated with other accretion indicators, suggesting an accretion origin. However, the line is blueshifted, which is inconsistent with its origin in an infall flow close to the star. It is possible that the complicated geometry of the region, as well as turbulence in the shock region, are responsible for the blueshifted line profiles.