Genetic selection for higher productivity increased dairy sheep susceptibility to diseases and environmental stressors, challenging their health and welfare status and production efficiency. Improving resilience to such stressors can enhance their ability to face these challenges without compromising productivity. Our objective was to estimate genomic heritability and perform genome-wide association studies (GWAS) to detect SNPs and candidate genes associated with three proxy traits for resilience (milk somatic cell count—SCC, lactation persistency—LP, body condition score—BCS) of Chios and Frizarta dairy ewes. We used genome-wide genotypes of 317 Chios and 346 Frizarta ewes. Individual records of milk yield and BCS, and milk samples were collected monthly for two consecutive milking periods; samples were analyzed to determine SCC. The LP was calculated as the regression coefficient of daily milk yield on days from lambing. Within breed, variance components analyses and GWAS were performed using genomic relatedness matrices in single-trait animal linear mixed models. Genomic-based heritability estimates were relatively high (BCS: h2 = 0.54 and 0.55, SCC: h2 = 0.25 and 0.38, LP: h2 = 0.43 and 0.45, for Chios and Frizarta ewes, respectively), compared to previous pedigree-based studies. The GWAS revealed 7 novel SNPs associated with the studied traits; one genome-wide and two suggestive significant SNPs for SCC (Frizarta: rs403061409, rs424064526 and rs428540973, on chromosomes 9, 1 and 12, respectively), one suggestive significant SNP for BCS (Chios: rs424834097 on chromosome 4) and three suggestive significant SNPs for LP (Frizarta: rs193632931 and rs412648955 on chromosomes 1 and 6, Chios: rs428128299 on chromosome 3). Nineteen candidate genes were detected: two for BCS (Chios: POT1, TMEM229A), thirteen for SCC (Frizarta: NTAQ1, ZHX1, ZHX2, LOC101109545, HAS2, DERL1, FAM83A, ATAD2, RBP7, FSTL1, CD80, HCLS1, GSK3B) and four for LP (Frizarta: GRID2, FAIM, CEP70—Chios: GRIP1). Present results show that resilience in the studied dairy sheep breeds is heritable and advance existing knowledge on the genomic background of SCC, LP, and BCS. Future research will quantify effects of different alleles of significant SNPs on the studied traits and search for possible correlations among traits to facilitate their effective incorporation in breeding programs aiming to improve resilience.