  We search for excess gamma-ray emission coincident with the positions of
confirmed and candidate Milky Way satellite galaxies using 6 years of data from
the Fermi Large Area Telescope (LAT). Our sample of 45 stellar systems includes
28 kinematically confirmed dark-matter-dominated dwarf spheroidal galaxies
(dSphs) and 17 recently discovered systems that have photometric
characteristics consistent with the population of known dSphs. For each of
these targets, the relative predicted gamma-ray flux due to dark matter
annihilation is taken from kinematic analysis if available, and estimated from
a distance-based scaling relation otherwise, assuming that the stellar systems
are dark-matter-dominated dSphs. LAT data coincident with four of the newly
discovered targets show a slight preference (each ~$2 \sigma$ local) for
gamma-ray emission in excess of the background. However, the ensemble of
derived gamma-ray flux upper limits for individual targets is consistent with
the expectation from analyzing random blank-sky regions, and a combined
analysis of the population of stellar systems yields no globally significant
excess (global significance $<1 \sigma$). Our analysis has increased
sensitivity compared to the analysis of 15 confirmed dSphs by Ackermann et al.
2015. The observed constraints on the dark matter annihilation cross section
are statistically consistent with the background expectation, improving by a
factor of ~2 for large dark matter masses ($m_{{\rm DM},b \bar b} \gtrsim 1$
TeV and $m_{{\rm DM},\tau^{+}\tau^{-}} \gtrsim 70$ GeV) and weakening by a
factor of ~1.5 at lower masses relative to previously observed limits.
