The performance of the approximate spin projected (AP) coupled cluster singles and doubles (CCSD) methods based on the spin-unrestricted Hartree-Fock and Brueckner determinants, namely AP-UCCSD and AP-UBD, is benchmarked for singlet-triplet energy gaps in various open-shell species. The test set includes the TS12 set, organic diradicals, and two binuclear copper complexes. We demonstrate that chemical accuracy (1 kcal/mol) can be reached for small open-shell molecules. These methods also provide highly accurate results for larger systems, in good agreement with the established equation of motion spin-flip CCSD (EOM-SF-CCSD) results.