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.
The power of buddha-dharma is revealed depending on whether or not there is effort, and is distinguished depending on whether or not it is practiced. - Dogen, "Guidelines for Studying the Way"
Namu Amida Butsu