  This is the second of a series of papers outlining an approach to the
classification of $\mathcal{N}{=}2$ superconformal field theories at rank 2 via
a systematic analysis of their Coulomb branches, mathematically described by
special K\"ahler scale invariant geometries. Here we describe how to make the
translation between geometry and field theory data. We apply this strategy to
the special K\"ahler geometries found in the first paper of the series where we
made strong simplifying assumptions on the form of the solutions. Remarkably,
we find that our bottom-up classification strategy pays off even in this
simplified setup. All scale invariant solutions in the first paper of the
series have an interpretation as the Coulomb branch of at least one
$\mathcal{N}{=}2$ superconformal field theory, many matching what is already
known. But we also predict the existence of six new rank 2 theories, including
an entire new set closed under renormalization group flow. We characterise and
discuss in detail each one of these new $\mathcal{N}{=}2$ superconformal field
theories. To our knowledge none of them have known string theoretic or higher
dimensional realisations.
