Solution techniques for dynamic contact problems, namely dynamic Signorini problems with and without friction, thermo-mechanical, and rolling contact problems, are discussed. Rothe`s method is used to discretise the problems. After discretisation in time with an adequate time stepping scheme, e. g. the Newmark method, which is studied exemplarily in this article, the semi discrete problems are solved by low order finite elements. The finite element discretisation is based on the solution techniques, which were described in the first part of this series of articles [H. Blum, H. Kleemann, A. Rademacher, A. Schröder: On Solving Frictional Contact Problems, Part I: Abstract Framework and the Static case]. Numerical results, including the application of the presented techniques to an example from production engineering, illustrate the performance of the presented techniques in every considered problem type.