Four years (2010-2014) of semiannual pointings by the Hubble Space Telescope Imaging Spectrograph (STIS) on nearby Alpha Centauri have yielded a detailed time history of far-ultraviolet (FUV: 1150-1700 Å) emissions of the solarlike primary (A: G2 V) and the cooler but more active secondary (B: K1 V). This period saw A climbing out of a prolonged coronal X-ray minimum, as documented contemporaneously by Chandra, while B was rising to, then falling from, a peak of its long-term (∼8 year) starspot cycle. The FUV fluxes of the primary were steady over most of the STIS period, although the [Fe xii] λ1242 coronal forbidden line (T∼ 1.5 MK) partly mirrored the slowly rising X-ray fluxes. The FUV emissions of the secondary more closely tracked the rise and fall of its coronal luminosities, especially the “hot lines” Si iv, C iv, and N v (T∼ 0.8-2 × 105 K), and coronal [Fe xii] itself. The hot lines of both stars were systematically redshifted, relative to narrow chromospheric emissions, by several km s-1, showing little change in amplitude over the four-year period, especially for α Cen B, despite the significant evolution of its coronal activity. Further, the hot lines of both stars, individually and epoch-averaged, displayed non-Gaussian shapes, which most trivially could be decomposed into two components, one narrow (FWHM ∼25-45 km s-1), the other broad (60-80 km s-1). A bimodal Gaussian strategy had been applied previously to the α Cen stars, but this was the first opportunity to evaluate any time dependence. In fact, not much variation of the component properties was seen, even over the major cycle changes of B. Curiously, the line fluxes were about equally divided between the narrow and broad components for both stars. The fact that there is minimal activity dependence of the narrow/broad flux partition, as well as densities derived from O iv] line ratios, either during the cycle evolution of B or between A and B, suggests that there is a dominant “quantum” of FUV surface activity that is relatively unchanged during the cycle, aside from the fractional area covered.