  We use 38 C IV quasar (QSO) reverberation-mapped (RM) observations, which
span eight orders of magnitude in luminosity and the redshift range $0.001064
\leq z \leq 3.368$, to simultaneously constrain cosmological-model and QSO
radius-luminosity ($R-L$) relation parameters in six cosmological models, using
an improved technique that more correctly accounts for the asymmetric errors
bars of the time-lag measurements. We find that $R-L$ relation parameters are
independent of the cosmological models used in the analysis and so the $R-L$
relation can be used to standardize the C IV QSOs. The C IV QSO cosmological
constraints are consistent with those from Mg II QSOs, allowing us to derive
joint C IV + Mg II QSO cosmological constraints which are consistent with
currently accelerated cosmological expansion, as well as consistent with
cosmological constraints derived using better-established baryon acoustic
oscillation (BAO) and Hubble parameter [$H(z)$] measurements. When jointly
analyzed with $H(z)$ + BAO data, current C IV + Mg II QSO data mildly tighten
current $H(z)$ + BAO data cosmological constraints.
