We verified the possibility of cooling peccary semen for 4, 24, and 48 h before cryopreservation, using different dilution media (TRIS + egg yolk (20%) and PRIMXcell Ultra). Ten ejaculates were divided equally into six aliquots and then diluted. Two aliquots were stored in a biological incubator (4 h), and the remaining aliquots were stored in a commercial container, the Botutainer® (24 and 48 h), both at 5 °C. The samples were cryopreserved and then evaluated for kinetic parameters, functionality, integrity, mitochondrial activity, morphology, and sperm binding capacity. After thawing, samples diluted in TRIS showed total motility of 43.4 ± 6.8%, 48.4 ± 6.2%, and 38.6 ± 5.0% after cooling for 4, 24, and 48 h before cryopreservation, respectively. Such results are significantly greater than those achieved with the use of PRIMXcell diluent for 4 (8.3 ± 2.8%), 24 (4.7 ± 1.4%), and 48 h (4.8 ± 2.9%) storage (p < 0.05). Furthermore, TRIS provided better preservation of sperm membrane integrity when samples were cooled for 24 h (44.5 ± 4.7%) before cryopreservation compared to those samples diluted in PRIMXcell Ultra stored for 24 (25.7 ± 4.0%) and 48 h (25.2 ± 4.0%) before freezing (p < 0.05). In summary, we suggest TRIS diluent + egg yolk (20%) as an effective option to allow semen to cool for 24 or 48 h in a transport container before cryopreservation.