Women often played a large role in pagan kings' decision to convert.

• Clovis, King of the Franks was convinced to abandon paganism by his wife, Saint Clotilde of Burgundy
• Æthelberht of Kent was converted by his wife, the Frankish princess, Saint Bertha.
• István I of Hungary and his father both agreed to convert so that he could marry Gisela of Bavaria, though István appears to have been a more faithful Christian than his father was.
• Mieszko I of Poland agreed to convert so that he could marry Doubravka of Bohemia.
• Vladimir the Great had a Christian grandmother, Saint Olga of Kiev, and finally agreed to convert so he could marry the Byzantine princess, Anna Porphyrogennētē
• Hermenegild I of the Visigoths was convinced to abandon Arianism by his wife, Ingund of Austrasia. (Though Arianism was a form of Christianity, it still fits the pattern).
• Władysław II Jagiełło agreed to convert to Catholicism so that he could marry Jadwiga of Poland and become king of Poland jure uxoris.

Two books I read recently, The Realm of Saint Steven and East Central Europe in the Middle Ages pointed out that converting often opened the door to Christian marriage alliances and that the idea of one god and one church often fit better with kings' missions to somewhat centralize their authority that the multitude of gods of pagan faiths.

It's difficult to judge what any of them were thinking psychologically, as ancient and medieval chroniclers generally did not seek to uncover their subjects' inner lives and motivations, as modern writers so often do.