In my Drupal 7 site, I have a URL pattern set for new blog posts of [node:og-group-ref:url:path]/blog/[node:title].
I want to create a rule for one organic group that when new posts are saved for that OG, there is a rule set that the path would automatically change to [node:og-group-ref:url:path]/archive/[node:title].
Any ideas on how to do that within the Rules module?
So, to answer your exact question. You CAN do it with the rules module.
Enable the rule module,
Construct the url alias at the bottom, using replacement patterns per your original answer.
You will be able to accomplish what you asked following this methodology.
Without knowing the exact specifics of the use case, there's also a chance you can do what you're looking to do with Pathauto alone