if your kingdom's army, which includes your vassals' parties, is large, it helps. if the potential vassal hates no one in your court, it helps. if you already have some of the lord's family by your side (wife counts) the odds improve. Be careful though - some lords hate a monarch who changes his argument too much. if you choose the right arguments, you will improve your odds. if you have high persuasion, you can improve your odds to convince someone. if you cultivate relationship before you declare yourself a monarch, lords will be more willing to join you even if you are weak. with high honor, saints (honorable, good-natured, benevolent, upstanding) will be inclined to join you, especially if their faction is destroyed. There are a number of things that influence the likelihood of them switching.
Lords who give you a chance to persuade them never have a 100% to turn. You could also try to destroy their relationship with their king, but that is harder, time consuming, and altogether inefficient. The only realistic way to have them as your vassals is to destroy their faction. Lords who say 'Long live the king!' are happy in their faction, either because of their saintly personality, or because of exemplary treatment by their liege.
