  Assuming the Riemann hypothesis, we establish an upper bound for the $2k$-th
discrete moment of the derivative of the Riemann zeta-function at nontrivial
zeros, where $k$ is a positive real number. Our upper bound agrees with
conjectures of Gonek and Hejhal and of Hughes, Keating, and O'Connell. This
sharpens a result of Milinovich. Our proof builds upon a method of Adam Harper
concerning continuous moments of the zeta-function on the critical line.
