My father will soon be niftar and buried, and there will not be a minyan. I know we can recite tehillim. Is there a prayer that can be recited that is similar to kaddish?

You should also recite the "El Maleh Rachamim" prayer found in siddurim (usually in Yizkor, right before the Musaf prayer of festivals), which doesn't require a minyan. May your father not suffer and leave this world for the world to come with nachas and with as little pain as possible.