Suāsōria means "intended to persuade", as an adjective, or "a speech intended to persuade", as a noun.
Suāsor is a noun meaning "someone who persuades or advises"; suāsōrī is the dative singular, meaning "to/for someone who persuades".
Pātrōnus is a noun meaning "defender" or "patron"; pātrōnum is the accusative singular, used as the direct object of a verb. It can also mean "advocate" in a legal context.
I'm not aware of any specifically Christian context for suāsor or suāsōria, but pātrōnum (as I imagine you're aware) shows up in the Diēs Īrae:
Quid sum, miser, tunc dictūrus?
Quem pātrōnum rogātūrus?
Cum vix justus sit secūrus?
[When the day of judgement comes…]
What is this poor wretch then supposed to say?
What advocate should I call upon,
when even the righteous can scarcely be sure [of salvation]?
The form here is pātrōnum instead of pātrōnus because it's the object of the verb "call upon" (rogō), indicating the person who is being called.
In this case, I would recommend pātrōnus instead of pātrōnum, since it's in the nominative or "default" case. But that's liable to be taken too.
Might I suggest pātrōcinium or pātrōcinia? This is an abstract noun formed from pātrōnus, changing the meaning from "advocate" to "advocacy" or "protection". (The former is singular, the latter is plural, but that distinction doesn't matter too much with this word.)
P.S. The lines over certain vowels can be included or left off, whichever you prefer; they indicate a difference in pronunciation that disappeared in later Latin.