janissaries
Ottomans did not take them by force. Christian families gave their childrens willingly. Think this, the Sultans relied upon the recruited janissaries for their own security. Janissaries were the protectors of the Sublime Port and main troops of the army. Now, how would the sultans trust them for the protection of their palace if they were taken out by force. Moreover, more than half of the grand viziers were recruited Christians, and they served the top post of the empire. Islam attracts many Christians even now when muslim nations are underdeveloped. And when muslims had powerful states Islam attracted more and more, peacefully of course. We are talking about a state that lasted 622 years. A state cannot last that long on sword.