Why were southern delegates to the constitutional convention willing to accept the three-fifths compromise?

Because it was better than nothing. They were slavers but they didn't consider slaves to be real people, but since it worked well for them to count them as population, they had a choice, either count them as people and break their own understanding of slavery but in return get political power, or not count them as people and lose political dominance due to the house of representatives being much smaller. In the end they accepted the three-fifths compromise.