In 2 levels my Paladin will be getting aura of protection adding +4 to all my character's saves. I am struggling between Infernal Constitution or Resilience CON as an ASI. In your games, does the resistance to cold and poison come up more than just having a higher con save?

I know that maintaining spell concentration is the big reason for Resilience CON, but my character will have a +2 from attribute, and the +4 from the aura. If I add Resilience CON it increases from +6 to +9.

Our game has been mostly orcs, ogres, and undead, but we are getting into dragons and some higher level opponents.

So, in my game cold hasn’t been an issue, poison wasn’t, but then last session, it was. Damage types are very much a campaign to campaign thing, so might not useful worrying about what anyone else deals with.  If those upcoming dragons are white or green, it will be great, but anything else, and not so much. 
Personally, I don’t try to meta game the resistances that might be best. There are certainly types that come up more often, but it’s very situational. And really wisdom is often more important so you don’t get dominated. 
If you are thinking about concentration, look at warcaster, which is great, though you don’t get the +1 from it, and you likely won’t use a cantrip for an OA, but otherwise it’s solid for a pally.
Honestly, a + 6 is a lot. A feat to get you to plus 9 kind of seems like overkill. 

 

Resilient Con is usually not necessary for paladins unless they've got an abnormally low charisma (in which case, boost your charisma).  Infernal Constitution grants resistance to two relatively common damage types- it's not usually the first thing I take for a tiefling character but it's one that's never not useful.  Of course, the other option if you're worried about concentration rolls specifically is War Caster- advantage with a +6 means that unless your dice hate you, you're not going to be failing much.

My gut says go for Resilient(Con). Yes, +10 to your Con saves is quite high. But if the DC is high enough that having a +10 instead of +6 makes a real difference, failing that Con save is going to SUCK. It will also help maintain Concentration on spells, which is always a good thing. Something else to consider, Cold and Poison damage often involve Con saves. So significantly increasing your odds of making those saves would likely give you at least some of the benefit of having resistance to those damage types, in addition to the other benefits of a high Con save bonus.

In this build, I built in a need for +1 CON to get from 13 to 14 constitution. That leaves these feats: Durable, Resilient, Tavern Brawler, or Infernal Constitution. Durable and Tavern Brawler are not really for my character, leaving Resilient or Infernal Constitution to choose from. I had planned on picking up Resilient, but then Infernal Constitution popped up on my radar. I was just wondering how other players experiences were with them.

I'd definitely go with Infernal Constitution there.  Your saves are already very good and resistance applies to effects that don't allow Con saves (or any saves), like Ray of Frost or being bitten by a green dragon.  And you also get advantage on saves against the Poisoned condition.

I think I am leaning toward Infernal Constitution as well. Both flavor and mechanics-wise. Being more of a devil sounds cooler. I also thought Warcaster just allowed advantage on concentration checks. After reading it, I see how it can be more valuable for a front line caster than a mere concentration check.

Warcaster's big advantage for a paladin is that it lets you cast spells with somatic components when you've got a weapon in your hand. Whether or not that's a big advantage depends on how much of a stickler your GM is for that rule.

Also, casting a smite spell on a opportunity attack if you need to. Or any other 1 action spell that might have a nice AoE, then allow you to still get your regular attack(s).

The smite spells don't let you attack, they have a range of Self, so you can't cast them on opportunity attacks.

The spell must have a casting time of 1 action and must target only that creature

That last bit of the sentence I did not focus on very well, darn. :-(