Sources for times that one can daven that a sick person should die:

  • Gemora Brochos 6a according to the version of the Gaonim
  • Gemora Kesuvos 104a
  • Gemora Taanis 23a (Choni Hamaagal)
  • Gemora Bava Metzia 84a (Rabbi Yochanan and Rish Lakish)
  • Sefer Chasidim: 519
  • Ran Nedarim 40a