  A new derivation of systemic proper motions of Milky Way satellites is
presented, and applied to 59 confirmed or candidate dwarf galaxy satellites
using Gaia Data Release 2. This constitutes all known Milky Way dwarf galaxies
(and likely candidates) as of May 2020 except the Magellanic Clouds, the Canis
Major and Hydra 1 stellar overdensities, and the tidally disrupting Bootes III
and Sagittarius dwarf galaxies. We derive systemic proper motions for the first
time for Indus 1, DES J0225+0304, Cetus 2, Pictor 2 and Leo T, but note that
the latter three rely on photometry that is of poorer quality than for the rest
of the sample. We cannot resolve a signal for Bootes 4, Cetus 3, Indus 2,
Pegasus 3, or Virgo 1. Our method is inspired by the maximum likelihood
approach of Pace & Li (2019) and examines simultaneously the spatial,
color-magnitude, and proper motion distribution of sources. Systemic proper
motions are derived without the need to identify confirmed radial velocity
members, although the proper motions of these stars, where available, are
incorporated into the analysis through a prior on the model. The associated
uncertainties on the systemic proper motions are on average a factor of $\sim
1.4$ smaller than existing literature values. Analysis of the implied
membership distribution of the satellites suggests we accurately identify
member stars with a contamination rate less than 1 in 20.
