Post navigation using date

If you’re trying to navigate between posts in the same category, would next_post_link()/previous_post_link() work for you?

These functions have an $in_same_cat argument, that would appear to suit your needs?

EDIT:

Here is a Plugin, WP Category Archives, that might point you in the right direction? It purports to display:

…a monthly or yearly archive of posts for one specific category. It is very similar to the WordPress Archive except that it just displays one specific category’s posts, not all categories. It can be configured to either show a listing or a pulldown by month or year with or without post counts.