I don't quite understand what you're asking. Do you mean the coefficient of variation for the within-subject effect (i.e., each subject's {measurement 1 vs. measurement 2} difference)? If so, you could just calculate the difference score for each subject, and then get the coefficient of variation of those difference scores using the normal formula (SD/mean).
If what is desired is just the standard deviation of the two variables for a given case divided by the mean of the two variables, just use the CFVAR function in COMPUTE. Transform>Compute and in the list of functions on the right it's there under All. If what is desired is a single value that's the standard deviation of the differences of the two variables divided by the mean difference, then it would require getting those two numbers and manually dividing. The easiest way would be to compute the difference variable, then use Data>Aggregate without a break variable and compute both the mean and SD of the computed difference variable, either writing those to a new data set or just back to the current file (where you would get them with the same overall value in every case), then compute the ratio.
actually I am myself not too sure about which formula I should apply. My goal is to use the CV for a responder analysis about a response that I observed in a experimental paradigm with a pretest and a posttest. I have included a control condition in the experiment, which I want to use as a reference for the responder analysis, meaning that I define individual changes that are greater than one CV I have obtained in the control condition as a response. Therefore, I need one value for the control condition. According to David, this is then is the standard deviation of the differences divided by the mean differences. Is that correct?