Sure there is. I'm assuming you're adding the Like buttons using the {JFBCLike} tag, but a similar solution is available with the modules too. Basically, each Like button is associated a specific URL. So, ideally, for each 'day' you'd have a new page that the Like would be associated with. I believe this can even be with separate 'jump' tags with the #, so you could do separate Like buttons with the following tags:
{JFBCLike url=http://www.site.com/updates#day1}
{JFBCLike url=http://www.site.com/updates#day2}
{JFBCLike url=http://www.site.com/updates#day3}
You'll have to test with the #day1 thing though, as it's possible Facebook will realize that's the 'same' page.. and instead, you'll have to use a 'fake' page instead like site.com/updates/day1
Hope that helps, but you can definitely have multiple Like's on the same page that aren't linked. We do this all the time with category blog layouts and other type views that reference multiple articles.
Keep us posted on how it goes, and good luck,
Alex
Mulitple likes on the same page
