And please don't suggest "Just play a normal cleric". The whole character's concept is based around a knowledge-focused, skilled and cloistered guy, and I'll just deal with the mechanical weakness of Diminished Spellcasting.
It doesn't say that he is proficient with his deity's favored weapon, either, though. Under the Cleric's weapon and armor proficiencies, it specifically states, "Clerics are also proficient with the favored weapon of their deity." Cloistered Cleric replaces a regular Cleric's weapon and armor proficiencies and does not say that they are proficient with the favored weapon.
I would rule that, no, Cloistered Cleric is not proficient with their deity's favored weapon. Check with your GM, though, he might allow it.
Over on the PFS General Discussion forums, we've had a recent rash of Rules questions, which then get shunted over here because they're about Pathfinder rules rather than things specific to PFS organized play. Thing is, the posters have complained about having their threads moved here, and even prefaced their posts with things like "Please don't move this to Rules Questions; all you ever get there is houserules, 'ask your GM' and people telling you you're stupid for asking".
Not trying to pick on you specifically, but I think it's a sad state of affairs when the Rules Questions section of the boards has such a reputation that people would actually prefer to take their rules questions to a different forum.
So please, everyone: if you're going to respond to a question in the Rules forum, answer in the context of the rules, even if you do things differently in your own games.
Alright I won't tell you to play a regular Cleric, instead I will tell you to play an Enlightened Philosopher Oracle of Life, one CC lover to another, in PF it's the better option
When an archetype replaces another ability you have to go with the new ability in its entirety. Thus when the CC section on weapons and armor proficiency replaces the existing weapons and armor proficiency you lose the deities weapon proficiency too.
If on the other hand it makes a statement such as 'in addition to their normal proficiencies' then you gain the new wording while not losing the old.