The Magellanic Clouds are the most massive and closest satellite galaxies of the Milky Way, with stars covering ages from a few Myr up to 13 Gyr. This makes them important for validating integrated light methods to study stellar populations and star-formation processes, which can be applied to more distant galaxies. We characterized a set of stellar clusters in the Small Magellanic Cloud (SMC), using the Southern Photometric Local Universe Survey. This is the first age (metallicity) determination for 11 (65) clusters of this sample. Through its 7 narrow bands, centered on important spectral features, and 5 broad bands, we can retrieve detailed information about stellar populations. We obtained ages and metallicities for all stellar clusters using the Bayesian spectral energy distribution fitting code BAGPIPES. With a sample of clusters in the color range −0.20 < r − z < +0.35, for which our determined parameters are most reliable, we modeled the age-metallicity relation of SMC. At any given age, the metallicities of SMC clusters are lower than those of both the Gaia Sausage-Enceladus disrupted dwarf galaxy and the Milky Way. In comparison with literature values, differences are Δlog(age) ≈ 0.31 and Δ[Fe/H] ≈ 0.41, which is comparable to low-resolution spectroscopy of individual stars. Finally, we confirm a previously known gradient, with younger clusters in the center and older ones preferentially located in the outermost regions. On the other hand, we found no evidence of a significant metallicity gradient.