Dry, sunny months combine low precipitation with high evaporative demand, so irrigation requirements depend on the joint behaviour of precipitation (P) and reference evaporation (E). This study evaluated the reliability of supplemental irrigation supply for grassland at three Dutch sites (De Bilt, 1980–2019; Heibloem, 1980–2016; Wageningen, 1976–1999) using monthly P and Makkink E. The net irrigation requirement (NIR) was computed for the growing season (April–September) and for the peak month (July). P and E were modelled with marginal distributions selected by the Anderson–Darling statistic, and their dependence with Gaussian, Frank and rotated Clayton and Gumbel copulas. The limit state compared a supply capacity with the NIR, which also depended on a crop factor, an effective rainfall fraction and the initial soil water. The first-order reliability method (FORM) with a Rosenblatt transformation was compared with the second-order method (SORM), Monte Carlo simulation (MCS) and importance sampling. Kendall’s τ between P and E was -0.26 to -0.17 for the season and -0.51 to -0.35 for July. Seasonal E increased significantly at all sites. For a capacity equal to the empirical 80% quantile of the NIR, the copula model gave failure probabilities of 0.197–0.244. Ignoring dependence underestimated them by 8–10% for the season and 32–43% for July. FORM errors ranged from -8.5% to +10.2% relative to MCS, whereas SORM was within 1.3%. The order of the Rosenblatt transformation changed the FORM importance factors considerably but the failure probability only slightly. Inverse FORM showed that neglecting dependence would undersize the capacity for 95% reliability by 3–11% (season) and 9–17% (July). Precipitation was the most important variable, followed by E and the crop factor. Copula-based reliability analysis with SORM or MCS verification is recommended for sizing irrigation supplies.