It is difficult to alter actual DNA tests, but one can do it by default. For example one can live the test in the sun too long and also having poor laboratory DNA measures can alter a DNA test. Under a different context, one can also deny the results especially if it is a court case.
2 Additional Answers
There is no way of altering the results of a paternity test. The only way that the test would show up a different parent is if there is a sample taking from another individual.
There is no way to alter a DNA test, the truth is in the DNA. You are who you are, and there is no altering that. However, depending on what the circumstances are, you may be able to deny a test.