Is there a rating for Chaplin's Assistant in the Coast Guard Reserve? If not, are there billets filled by Naval Reservists at Coast Guard stations?

No and No

The USN Reserve does have chaplains, both commissioned and enlisted (religious program specialist). These Reserve chaplains can be stationed at a USCG unit. As I understand, currently there are only a dozen or two (Navy) chaplains in the whole CG. You could check through a Navy recruiter to see what the options are in your area.

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Is there a rating for Chaplin's Assistant in the Coast Guard Reserve? If not, are there billets filled by Naval Reservists at Coast Guard stations?

No chaplains assistants in the Coast Guard. You'll need to be in the Navy for that. CPO Kalbach