thedarkwanderer’s answer seems to me to be a pretty good list of options for this, as-written.
But I think you should seriously consider deviating from things as they’re written here. Alignment is a deeply problematic part of the game for a variety of reasons, and I have long advocated for just ignoring it as much as possible. I think it is very bad for the game that divine grace is the unique province of lawful-good characters: it diminishes the diversity of the game.
Certainly, there is no mechanical balance need for strict alignment requirements. There is a slight corner case here (a CG paladin could take Desna’s Divine Fighting Technique to get both divine grace and the ability to use Cha for attack and damage with starknives—but then note that this clashes with how smite evil works and is actually not as good as it first seems, plus if you aren’t playing in Golarion, that DFT might very well be associated with an LG deity anyway), but that’s literally the worst of it. Otherwise, it’s trivial to just allow paladins of every alignment, with smite evil changing as necessary for the chosen alignment. (For that matter, even with the improvements to smite evil in Pathfinder, it would still be perfectly safe to allow paladins to just smite any foe—after all, plenty of paladins play in campaigns in which all their enemies are evil, and that doesn’t make them overpowered.)
So I would try asking your GM about doing a CG paladin, and it’s my personal (strongly-held) opinion that your game would be better if he or she allowed you to. You have a character in mind that you want to play who is best represented in the game’s mechanics using the paladin’s class feature. I do not think there is any good reason that a GM should prevent you from doing that.