As said, worked examples of possible alternatives include the 5e monk (ki points,) 5e sorcerer (metamagic,) 5e warlock (varying able to modify Eldritch Blast,) and 4e Psionic Classes.
Reading some of the 5e24 previews, similar ideas have been used for other classes (such as the rogue being able to spend sneak attack dice for other effects).
The Paladin could have "Piety Points" (or whatever name you prefer). Those points would be used to power and modify Divine Smite. As such, none of the Smite spells would need to exist. (As I understand it, the 5e24 rules already treat Smite Spells differently, as they do not interact with Initiate Feats; the Bard's ability to pick up spells from other classes; and etc.)
Where the monk uses points to be a mobile attacker and spread damage around, the paladin would use them to pile damage onto a single target, heal, and protect allies.
Auras, Lay on Hands, Channel. Divinity, save bonuses, and Divine Sense all already worked without using spell slots. It doesn't seem like a giant leap in design to also have Divine Smite (which was not a spell) function in a way that doesn't use spell slots and is instead more like the rest of the class. If you really wanted a small handful of Paladin spells, they could just as easily be powered by spending points.
That may not be your personal cup of tea, and that's valid.
Do you feel that your personal preferences included a desire for the Paladin to become more of a vancian caster?
