  The spectra of singly ionised Strontium and Yttrium (Sr {\sc ii} and Y {\sc
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 {\sc ii} and Y {\sc
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
{\sc tardis} and {\sc 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 {\sc ii} and Y {\sc 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 {\sc
tardis} reveal no new significant changes to the full synthetic spectra. NLTE
simulations in {\sc 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.
