Purchase a copy of the "Poet's Market" and formulate a list of your publishing options. The "Poet's Market" is a resource book for poets that includes a large section on Christian poetry markets, which lists publishers who accept Christian poetry and gives complete contact details and submission guidelines. Compiling a list of suitable markets for your work from this book is the most effective way to find paying markets for your Christian poetry.
Search the internet for online Christian poem publishing markets and associations for Christian writers. Because the market for Christian poetry is narrow in comparison to other types of writing, getting involved in a Christian writer's association can help you build a strong network. In Christian writing, the atmosphere of fellowship is such that other writers share ideas and publishing venues. A strong network will be invaluable for getting your work in print or performed at Christian events.
Contact Christian churches and organizations with a short letter of introduction. The letter should be brief and give a short bio of you and your writing credits. Offer to allow the church or organization to publish your poetry in church newsletters or in weekly church handouts. This publishing avenue will likely not be a paying opportunity, but it's an effective way to publish your Christian-oriented work to a wide audience. This visibility can help you build your name as a Christian poet, which helps build your resume.