Milk color and processing traits are important factors informing the potential and ease to manufacture milk into different dairy products. The objective of the present study was to estimate (co)variance components of milk lightness (L*), redness-greenness (a*), yellowness-blueness (b*), rennet coagulation time (RCT), curd-firming time (k₂₀), curd firmness (a₃₀ and a₆₀), heat coagulation time (HCT), casein micelle size (CMS), and pH, measured by mid-infrared spectroscopy on 136,807 test-day records from 9,824 Irish dairy cows between 5 and 305 d-in-milk (DIM) from parities ≤ 10. Cow breed was defined as the proportion of Holstein, Friesian, Jersey, Norwegian Red, Montbéliarde, and “Other.” Random regression models using Legendre polynomials were performed to describe the change of both additive genetic and within-lactation permanent environmental variances across different DIM. Heritability estimates averaged across all DIM for milk color were 0.31 (L*), 0.11 (a*), and 0.42 (b*); average heritability estimates for processing traits ranged from 0.31 (pH) to 0.49 (k₂₀), except for HCT (0.17). Within-trait genetic correlations approached unity between adjacent DIM, and were <0.40 at the peripheries of lactation. Eigenvalues and associated eigenfunctions of the additive genetic variance of all traits revealed that at least 80% of the total variation was associated with the height of the lactation profile. Average genetic correlations between color traits across all DIM were the weakest between a* and b* (−0.19); fat concentration was strongly genetically associated with b* (0.91), while milk yield was negatively genetically correlated with all color traits. On average, RCT was strongly genetically correlated with both a₃₀ (−0.68) and pH (0.75); genetic correlations between HCT and the other processing traits were, on average, weak ranging from −0.02 (with pH) to 0.28 (with RCT). Milk yield was genetically correlated with both RCT (0.31) and a₃₀ (−0.49). Breeding for milk color and processing traits is possible but with some negative impact on genetic gain for milk yield.