  We consider dilaton gravity theories in four spacetime dimensions
parametrised by a constant $a$, which controls the dilaton coupling, and
construct new exact solutions. We first generalise the C-metric of
Einstein-Maxwell theory ($a=0$) to solutions corresponding to oppositely
charged dilaton black holes undergoing uniform acceleration for general $a$. We
next develop a solution generating technique which allows us to ``embed" the
dilaton C-metrics in magnetic dilaton Melvin backgrounds, thus generalising the
Ernst metric of Einstein-Maxwell theory. By adjusting the parameters
appropriately, it is possible to eliminate the nodal singularities of the
dilaton C-metrics. For $a<1$ (but not for $a\ge 1$), it is possible to further
restrict the parameters so that the dilaton Ernst solutions have a smooth
euclidean section with topology $S^2\times S^2-{\rm\{pt\}}$, corresponding to
instantons describing the pair production of dilaton black holes in a magnetic
field. A different restriction on the parameters leads to smooth instantons for
all values of $a$ with topology $S^2\times \R^2$.
