I actaully wrote a Seminary paper on this topic a few years ago (ie making churches/worship spaces truly accessible to those who are low vision/blind, Hoh/Deaf and have mobility challenges (wheelchairs, walkers, canes, balance etc) !!
On thing to do is contact your local ASL interpreter service - they won't supply CART, but should know who does.
The advantage of CART is that it can actually service the entire congregation as well as the HOh/Deaf individuals (provided they are comfortable using CART versus ASL interpreters). One thing worth mentioning and factoring into getting CART is that it's VERY likely that you may find that the congregation likes CART as well ... there are a LOT of HOh persons (age related) in churches who will benefit from CART, but are embarrassed to ask for assistance (or unaware things like CART even exist !!)
The disadvantage to CART is that some people (who's primary language is ASL) will struggle to understand what is being said via CART (because English is their Second or Third Language) - in this case ASL interpreters are better suited. The best thing to do is make sure that the services you are getting, are what will best suit the end users (the Hoh/Deaf individuals).
If there is no way that you are able to get CART ... one option is having everything pre-input (entire liturgy, songs, all scripture readings, the entire sermon/homily, all announcements, etc) on powerpoint (or similar) ... then have the slides displayed on a screen (either a permanent one on the wall, or a free standing kind) ... just make sure the powerpoint is in sync with the speech/song etc! Break songs up into verses, sermons into paragraphs (or less) etc ....
Using powerpoint is NOT as good as using CART and shouldn't be seen as a "cheap workaround" ... however it is better than nothing (powerpoint also it lacks flexibility, having words displayed "Real-time" which allows CART users to follow along with the congregation, "Get" the info/jokes/message etc at the same time etc)
If you do use powerpoint - avoid "flashy" fonts (use Tahoma, which is best for low vision), stick with plain text on plain background (white with bold black text, black background with yellow text etc ) ... it's meant to be easy to quickly read, not "decorative" - and while "fancying up" fonts and backgrounds etc my visually "look nice" the functionality/usability suffers for it.