The spectra of singly ionised Strontium and Yttrium (Sr ii and Y ii) have been proposed as identifications of certain spectral features in the AT2017gfo spectrum. With the growing demand for NLTE simulations of Kilonovae, there is a increasing need for atomic data for these and other r-process elements. Our goal is to expand upon the current set of atomic data for r-process elements, by presenting transition probabilities and Maxwellian-averaged effective collision strengths for Sr ii and Y ii. The Breit-Pauli and DARC R-matrix codes are employed to calculate the appropriate collision strengths, which are thermally averaged according to a Maxwellian distribution to calculate excitation and de-excitation rates. The tardis and ColRadPy packages are subsequently used to perform LTE and NLTE modelling respectively. A complete set of transition probabilities and effective collision strengths involving levels for Sr ii and Y ii have been calculated for temperature ranges compatible with kilonova plasma conditions. Forbidden transitions were found to disagree heavily with the Axelrod approximation, an approximation which is currently employed by other models within the literature. Theoretically important spectral lines are identified with both LTE and NLTE modelling codes. LTE simulations in tardis reveal no new significant changes to the full synthetic spectra. NLTE simulations in ColRadPy provide indications of which features are expected to be strong for a range of regimes, and we include luminosity estimates. Synthetic emission spectra over KNe densities and temperatures reveal potentially interesting spectral lines in the NIR.