Not sure what this has to do with CBSubs; thread moved to GroupJive boards, but CB nor GroupJive provide event scheduling. Extensions such as jEvents or Eventlist are perfectly acceptable. GroupJive can provide the Group based usage.

With release of GJ 2.0 (on or before 28th this month we hope) it's possible to create Events within Groups. So basically with GJ 2.0 (not yet released!) you'll be able to have what you're wanting (no calendar is provided though).

Again, GJ 2.0 (when released) will have events support; this means users individual Church groups will be able to schedule events for their group (their Church) for users to attend. Aside from this you've available extensions such as jEvents or Eventlist or any other event extension. CB it self has no events scheduling, sorry.

I need to know if there is ANY way to do this with CB at this time.

The groups aspect, yes. The calendar, no; you'll need a 3rd party extension such as jEvents or Eventlist. Pretty much any extension should work with CB, whether it has a CB specific integration or not I can't say; this is a trial and error process you must perform when building a list of preferred extensions.