I once heard that only European nations have peacefully embraced Christianity. Is this true? Were there ever any Asian or African nations that converted to Christianity?

I'm not sure you can classify any European country as peacefully embracing Christianity But that is a question for another post.

Christianity originated in Asia. Israel is located in what we consider Asia. The first nation to make Christianity a national religion is Armenia located in Asia. The Armenian Apostolic Church

Shortly after or maybe even a little before Armenia claimed the title of first. The Abyssinian Church Became the state religion of Ethiopia in East Africa.

Sometime around 330 AD, the exact date is much in debate some claiming it was the majority earlier, The Christian Coptic Orthodox Church Of Egypt became the largest religion in Egypt.

Around this same time 330 AD Constantine was allowing Christianity to flourish from his capital in Constantinople. From this region springs The Eastern Orthodox Church

In 380 AD Christianity became the religion of Rome which at the time ruled much of north Africa beyond just Egypt.

In 451 the Oriental Orthodox Churches Split from the Eastern Orthodox Church. The Armenian and Ethiopian churches belong to this group but also groups from the areas that are now Iraq and Iran.

Several kingdoms in India also embraced Christianity at different points. We tend to think of India as a single monolithic entity but it was a group of small countries for much of its history.

Russia in Asia was primarily Eastern Orthodox before it became the USSR.

Tonga in the Pacific peacefully embraced Christianity in the 19th century.

This is just the briefest overview. I've left out many other examples which I hope some of our other experts can touch on. However, I think it's safe to say that Christianity spread "mostly peacefully" throughout large parts of Africa and Asia.