Precision measurements of superallowed Fermi β-decay transitions, particularly for the lightest superallowed emitters ^{10}C and ^{14}O, set stringent limits on possible scalar current contributions to the weak interaction. In the present work, a discrepancy between recent measurements of the ^{10}C half-life is addressed through two high-precision half-life measurements, via γ-ray photopeak and β counting, that yield consistent results for the ^{10}C half-life of T_{1/2}=19.2969±0.0074 s and T_{1/2}=19.3009±0.0017 s, respectively. The latter is the most precise superallowed β-decay half-life measurement reported to date and the first to achieve a relative precision below 10^{-4}. A fit to the world superallowed β-decay data including the ^{10}C half-life measurements reported here yields b_{F}=-0.0018±0.0021 (68% C.L.) for the Fierz interference term and C_{S}/C_{V}=+0.0009±0.0011 for the ratio of the weak scalar to vector couplings assuming left-handed neutrinos.