The usage of "A.D." or "Anno Domini" or "In the Year of the Lord" by the government is clearly Constitutional, for two reasons: it is standard practice in society (where the usage is not seen as implying any acceptance or endorsement of any religious belief--atheists commonly use it), and there is no law, that has any religious purpose, that requires anyone to use any of those phrases.
The California law that was ruled unconstitutional by the Ninth Circuit is a different matter altogether. A law requiring a recital of words that imply belief in God is not the same thing at all as the occurrence of the word "God" in some government document. For example, it would be Constitutional for Congress to pass a law that would forbid the words "In God We Trust" from appearing on legal tender. This clearly shows that the mere occurrence of the word "God" on government documents is not the issue.
It not a law requiring each student to say the pledge. They have the option not to recite it. They are not being forced to recite it. They just don't want their child to make that choice. It would be to difficult for them to do.
If this not the issue, then what are the atheists all upset about. They don't won't God anywhere, especially in the government, in words or on paper.