I always use this approach to adjust the contact stiffness in CalculiX: Snap-fit contact snagging problem - #17 by JuanP74 - Analysis issues - CalculiX (official versions are on www.calculix.de, the official GitHub repository is at https://github.com/Dhondtguido/CalculiX).
You will also find other tips regarding contact in rhat thread. And in this thread as well as the one linked there: Selection master and slave in contact
Contact damping is available in CalculiX (but not implemented in PrePoMax so requires the use of the Keyword Editor). It’s limited to implicit dynamics. This step type quite often has convergence issues in CalculiX, especially without appropriate global damping.
Contact damping syntax is described here: https://www.dhondt.de/ccx_2.23.pdf#subsection.7.19
Non-convergence in contact is often caused by initial rigid body motions in underconstrained models. Using symmetry (if applicable) and displacement control often helps.