Don't use repeating fields, instead set up a portal of related records. Not only will this enable you to select alternating row colors for your portal, but you'll have a much more flexible design that will make many other data operations much simpler.
Yes, I read a bit about this and saw that you could alternate row colours in a portal but then when I went to investigate portals further, I got thoroughly confused! Too complicated for me, a novice user :-(
I heartily recomend that you learn how to work with portals. This is FileMaker's number one tool for working with groups of related records. If you can master it, it will open many new and more powerful options for working with your data.
If you want, describe your database and I'll take a swing at getting you started with a portal that eliminates your repeating fields.