...This is a "template" website to be re-branded for multiple affiliates...I'm worried that these sites will be marked as duplicate content as most of the content will be the exact same for all, except for some different images, colors and text.
Sorry to burst your marketing or sharing tactic, but the sad truth is that if you create a template based website and everyone uses it and changes maybe one or two lines of it, only one copy will be indexed because users will be frustrated if they see dozens of duplicated pages in search results.
The solution seems to be a canonical reference to one of these white labels, but this will result in the other sites not being indexed. Is there a different way to mark these affiliate sites as "alternates", while still maintaining SEO for each one?
There's a wonderful way. I mean if you want, you can copy things from another site (a.k.a. template) to a minimal extent. This means if you want to use the same drop-down menu style as another site then do so, but your content (a.k.a. text) must be different because people are searching for useful information online.
The meta tag rel="alternate" seemed to be exactly what I was looking for, but this is apparently mostly used for localization and such. Any advice on this?
Alternate means "alternative version of the same thing". It's an old fashioned version of canonical that is recognized by more web browsers.
As I mentioned, instead of looking for one word to fix your issue, you need to treat templates as visual layout items. Once you pass your template on to others, then they will fill up the relevant sections of the template with text only relevant to their website ideas.
Color scheme is not an issue, however I'd suggest that if you modify the colours, you make the text color BLACK if you use a light background. Light grey text on white is the worst.