Weather prediction and climate simulations need reliable parameterizations of turbulent fluxes in the stable surface layer. Especially in these conditions, the uncertainties of such parametrizations are still large. Most of them rely on the Monin-Obukhov similarity theory (MOST), for which universal stability functions (SFs) represent important ingredients. The SFs are nonlinear, if so, a numerical iteration of the MOST equations is required. Moreover, presently available SFs are significantly different at large stability. To simplify the calculations, a non-iterative parametrization of fluxes is derived and corresponding bulk transfer coefficients for momentum and heat for a package of five pairs of state-of-the-art SFs are proposed. For the first time, a parametrization of the related transfer coefficients is derived in a universal framework for all package members. The new parametrizations provide a basis for a cheap systematic study of the impact of surface layer turbulent fluxes in weather prediction and climate models.