We present a novel way to organise the finite size spectra of a class of conformal field theories (CFT) with or (nonlinear) superconformal symmetry. Generalising the spinon basis of the WZW theories, we introduce supersymmetric spinons , 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 of (discrete) momenta. The state-content for given choice of is determined through a generalised exclusion principle, similar to Haldane's ‘motif’ rules for the theories. In the simplest case, which is the superconformal theory with central charge c = 1, we develop an algebraic framework similar to the Yangian symmetry of the theory. It includes an operator H2, 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 superconformal CFTs, this finitisation precisely leads to the so-called Mk supersymmetric lattice models with characteristic order-k exclusion rules on the lattice. Finitising the c = 2 CFT with nonlinear superconformal symmetry similarly gives lattice model partition sums for spin-full Fermions with on-site and nearest neighbour exclusion.