I think this would depend on the particular school and department you are considering applying to. That being said, if you already have taken some computer science courses as part of your undergraduate degree in math and have otherwise met the admission requirements for the program, I don't foresee any problems with your being admitted to and earning a second Master's degree in computer science.
My suggestion would be to visit the website of the computer science department of the school you wish to apply to and check their admission requirements. Also try to speak to a registrar about any other specific questions you may have.
You don't need any one degree for a graduate program typically. You do need to competency in the subject.
Since you already have a bachelors and masters, the next step would be to show you have taken (and understood) the required courses. This will vary from department to department.