If I recall, the Dalai Lama generally advises against conversion, using the analogy that it's better to dig one well fifty feet deep than ten wells five feet deep. I also know of several people who have married their Christian faith with Buddhist teachings. Unless you're an evangelical literalist, there's very little that conflicts in my opinion. Thomas Merton is an example, and he's written very insightfully about Zen and Catholicism. You may also benefit from looking into the contemplation practices of Christianity, such as St. John of the Cross.
Namu Amida Butsu
"When people of the Pure Land school chant Namu amida butsu, they are doing zazen with their mouths, and when we do zazen, we are performing Namu amida butsu with our whole body." - Kosho Uchiyama (Opening the Hand of Thought)