Deoxyribozymes (DNA enzymes) have been developed for a growing variety of chemical reactions, including with peptide substrates. We recently described the first tyrosine kinase deoxyribozymes, which lacked the ability to discriminate among peptide substrates on the basis of the amino acids surrounding the tyrosine residue. Those deoxyribozymes were identified by in vitro selection using a DNA-anchored peptide substrate in which the residues neighboring tyrosine were all alanine. Here, we performed in vitro selection for tyrosine kinase activity using three peptide substrates in which the neighboring residues included a variety of side chains. For one of these three peptides, we found numerous deoxyribozymes that discriminate strongly in favor of phosphorylating tyrosine when the surrounding residues are specifically those used in the selection process. Three different short peptide sequence motifs of 2-4 amino acids were required for catalysis by three unique deoxyribozymes. For a second peptide substrate, the selection process led to one deoxyribozyme which exhibits partial discrimination among peptide sequences. These findings establish the feasibility of identifying DNA enzymes that catalyze sequence-selective tyrosine phosphorylation, which suggests the downstream practical utility of such deoxyribozymes. More broadly, this outcome reinforces the conclusion that nucleic acid catalysts can discriminate among peptide substrates in the context of biochemically relevant reactions.