Discontinuous transcription has been described for different mammalian cell lines and numerous promoters. However, our knowledge of how the activity of individual promoters is adjusted by dynamic signaling inputs from transcription factors is limited. To address this question, we characterized the activity of selected target genes that are regulated by pulsatile accumulation of the tumor suppressor p53 in response to ionizing radiation. We performed time-resolved measurements of gene expression at the single-cell level by smFISH and used the resulting data to inform a mathematical model of promoter activity. We found that p53 target promoters are regulated by frequency modulation of stochastic bursting and can be grouped along three archetypes of gene expression. The occurrence of these archetypes cannot solely be explained by nuclear p53 abundance or promoter binding of total p53. Instead, we provide evidence that the time-varying acetylation state of p53’s C-terminal lysine residues is critical for gene-specific regulation of stochastic bursting.