What do you mean by VI Logger? The easiest way to do what you need is to create a while loop and put in it one of NI's "easy-IO" analog input VIs and a wait function set to 60,000 milliseconds. Depending upon the acquisition VI you use the result would read either one point, or a set of predefined points once a minute. (see attached code)
How much more complicated the application would get depends on such things as what exactly you want to do with the data, and how you want the user interface to react. For example do you need to save the data? If so, you'll need to add a file save function to the loop too. Also, the simple version I attached could take as long as 2 minutes to quit once you press the stop button--which probibly wouldn't be acceptable.
The point is that the basic functionality you asked for is very easy to do. The complicated part is defining all the other stuff that wraps around that simple functionality.
Mike...