Note: You will find Pope Pius XI's encyclical on atheistic communism, Divini Redemptoris (Divine Redeemer) useful in understanding what the Church teaches on the topic.
Cardinal Kung Foundation, The
The mission of The Cardinal Kung Foundation is to promote the Catholic Church in China which has endured many decades of persecution in this communist country It has had to go underground in a figurative way as much as the early Catholic Church had to go to the catacombs in a literal way.
You will find much information on the authentic Catholic Church in China (which is illegal) as well as the government-established Chinese Catholic Patriotic Association (which is not in communion with the Pope). The site also has information on the Underground Catholic Handicapped Orphanage; Cardinal Kung; many beautiful prayers, including a Prayer to Our Lady of Sheshan by Pope Benedict XVI; and a partial list of religious prisoners.
Cardinal Mindszenty Foundation
Here you will find much information on "the nature, propaganda and goals of atheistic Communism". Archives of their newsletter, The Mindszenty Report, are available from 1998 to the present. A few of the topics the Report covers are Marxism, secular humanism, Islam, Mother Teresa, Our Lady of Guadalupe, Saul Alinsky, the over-population myth, and "riveting files" on a spying case.