Hydroxylamine (NH$_{2}$OH) and methylamine (CH$_{3}$NH$_{2}$) have both been suggested as precursors to the formation of amino acids and are therefore of interest to prebiotic chemistry. Their presence in interstellar space and formation mechanisms, however, are not well established. We aim to detect both amines and their potential precursor molecules NO, N$_{2}$O and CH$_{2}$NH towards the low-mass protostellar binary IRAS 16293--2422, in order to investigate their presence and constrain their interstellar formation mechanisms around a young Sun-like protostar. ALMA observations from the unbiased, high angular resolution and sensitivity Protostellar Interferometric Line Survey (PILS) are used. Spectral transitions of the molecules under investigation are searched for with the CASSIS line analysis software. CH$_2$NH and N$_{2}$O are detected for the first time towards a low-mass source, the latter molecule through confirmation with the single-dish TIMASSS survey. NO is also detected. CH$_{3}$NH$_{2}$ and NH$_{2}$OH are not detected and stringent upper limit column densities are determined. The non-detection of CH$_{3}$NH$_{2}$ and NH$_{2}$OH limits the importance of formation routes to amino acids involving these species. The detection of CH$_{2}$NH makes amino acid formation routes starting from this molecule plausible. The low abundances of CH$_2$NH and CH$_{3}$NH$_{2}$ compared to Sgr B2 indicate that different physical conditions influence their formation in low- and high-mass sources.< Réduire