This looked like an easy task until I tried to pen it down. I know that 'Jezi vivan' means 'Jesus is alive', but how would you say 'My Jesus is alive'? ...Jezi m vivan ?

If you're going to use the contraction "m", then you should say it with the article: Jezi m nan vivan.
My Jesus is alive.
Jezi mwen an vivan. (non contracted)
Jezi m nan vivan. (contracted)
Haitian Creole ↔ English Reference, Look up Haitian Creole and English Words