  We present a novel way to organise the finite size spectra of a class of
conformal field theories (CFT) with $\mathcal{N}=2$ or (non-linear)
$\mathcal{N}=4$ superconformal symmetry. Generalising the spinon basis of the
$SU(n)_1$ WZW theories, we introduce supersymmetric spinons $(\phi^-,
\phi^{+})$, which form a representation of the supersymmetry algebra. In each
case, we show how to construct a multi-spinon basis of the chiral CFT spectra.
The multi-spinon states are labelled by a collection $\{ n_j \}$ of (discrete)
momenta. The state-content for given choice of $\{ n_j \}$ is determined
through a generalised exclusion principle, similar to Haldane's `motif' rules
for the $SU(n)_1$ theories. In the simplest case, which is the ${\cal N}=2$
superconformal theory with central charge $c=1$, we develop an algebraic
framework similar to the Yangian symmetry of the $SU(2)_1$ theory. It includes
an operator $H_2$, akin to a CFT Haldane-Shastry Hamiltonian, which is
diagonalised by multi-spinon states. In all cases studied, we obtain finite
partition sums by capping the spinon-momenta to some finite value. For the
$\mathcal{N}=2$ superconformal CFTs, this finitisation precisely leads to the
so-called M$_k$ supersymmetric lattice models with characteristic order-$k$
exclusion rules on the lattice. Finitising the $c=2$ CFT with non-linear ${\cal
N}=4$ superconformal symmetry similarly gives lattice model partition sums for
spin-full fermions with on-site and nearest neighbour exclusion.
