Does a school have any right by law to say if a student that writes for the school newspaper page can or cannot put anything about "God" in it?
I agree with the above post, and also would like to point out that a key difference between school newspapers and privately owned ones is that public tax dollars are used for its publication, and it is typically distributed to the student body free of charge. Within that context, students do not have absolute freedom of the press (regrettably, in my opinion) and the public, through their elected school board members, can exert an influence over what is allowable in terms of stories and content.
While barring any discussion of God or religion seems a bit extreme, and it does matter in what part of the paper it is printed (editorial? feature?), the school does, as per the Hazelwood decision, have the ultimate editorial authority over the content of the newspaper.
To some degree, they even have authority over what is written by students about the school and school personnel on private blogs, social networking sites and message boards, so the courts have typically given schools quite a bit of power at censoring student-published content.
Depending on the circumstances, a school may well have legal authority to do this. The controlling case here (the Supreme Court case that sets out the rule that applies) is Hazelwood v. Kuhlemeier (see link below).
The basic idea here is that a school newspaper is a school sponsored activity. Anything that is printed in the newspaper is presumed to be approved of by the school. Based on this idea, there is a possible reason to ban references to God.
That said, it would be important to know what is said and in what context. The Hazelwood case said that a school could ban articles that were not in keeping with the educational mission of the school. But that does not necessarily mean that a school could ban all mention of God. If, for example, a paper did a story about a student who had gone to Haiti on a mission and the student mentioned God, it would probably not be legal for the school to censor the article.
So this is not a clear cut case, based on the description you give -- more information would be useful.
I guess that depends, then, whether or not your teacher has any control over what you write for the paper. Are the stories previewed or graded by the teacher or do you write independently of the school? It would seem to me, without knowing the details here, that the paper is privately owned, and the page or section editor you write for would have the final say as to whether or not you could include Christian references or not, as opposed to your school. It might also make a difference what kind of story it is.
We have a similar program in my town, and religious references in student stories are common.
The paper is privately owned and the articles are not graded. We are just allowed to write something then turn it in and our teacher that is in charge reads over them for grammar and spelling and stuff like that.