We have searched for flavor-changing neutral current decays and lepton-number-violating decays of D^+ and D^+_s mesons to final states of the form h^+- e^-+ e^+, where h is either pi or K. We use the complete samples of CLEO-c open-charm data, corresponding to integrated luminosities of 818 pb^-1 at the center-of-mass energy E_CM = 3.774 GeV containing 2.4 x 10^6 D^+D^- pairs and 602 pb^-1 at E_CM = 4.170 GeV containing 0.6 x 10^6 D^*+-_s D^-+_s pairs. No signal is observed in any channel, and we obtain 90% confidence level upper limits on branching fractions B(D^+ --> pi^+ e^+ e^-) < 5.9 x 10^-6, B(D^+ --> pi^- e^+ e^+) < 1.1 x 10^-6, B(D^+ --> K^+ e^+ e^-) < 3.0 x 10^-6, B(D^+ --> K^- e^+ e^+) < 3.5 x 10^-6, B(D^+_s --> pi^+ e^+ e^-) < 2.2 x 10^-5, B(D^+_s --> pi^- e^+ e^+) < 1.8 x 10^-5, B(D^+_s --> K^+ e^+ e^-) < 5.2 x 10^-5, and B(D^+_s --> K^- e^+ e^+) < 1.7 x 10^-5.
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