Phosphorylates the deoxyribonucleosides deoxycytidine, deoxyguanosine and deoxyadenosine. 2'-deoxycytidine + a ribonucleoside 5'-triphosphate = a ribonucleoside 5'-diphosphate + dCMP + H(+) 2'-deoxyadenosine + ATP = ADP + dAMP + H(+) 2'-deoxyguanosine + ATP = ADP + dGMP + H(+) Homodimer. Phosphorylated and activated in vitro upon phosphorylation at Ser-74 by CSNK1D/CK1. Belongs to the DCK/DGK family.