Without the efforts of the various Churches in PNG education would grind to a halt. There are too many schools to mention them all but here are some of the tertiary ones.
The United Church runs the Gaulim Teachers College and the Rarongo Theological College both in East New Britain. They also have a nursing school at Salamo in Milne Bay
The Seventh Day Adventist Church has the well established university outside of Port Moresby called the Pacific Adventist University (PAU)
The two Lutheran Churches run the Balob Teachers College and the Martin Luther Seminary both in Lae.
The Catholic church runs the Divine Word University in Madang.
The government runs four universities in PNG:
University of Papua New Guinea; the University of Technology in Lae;
Goroka University in Goroka, which trains secondary school teachers; and
Vudal University in Rabaul, which trains people for the agricultural sector.
I am sure I have missed out other ones and I have not attempted to mention any of the primary or secondary schools.
Of course Anglican Priests are trained at Newton Theological College, just outside Popondetta in Oro Province.