
QuidEst |

Sense Motive does nothing, because there is nothing other than your Wisdom score and HD involved in the DC.
Cynical Ear is +2 DC for anybody. Also adds to diplomacy DC, for what it's worth.
Unflappable Arrogance is for Ifrits, and adds +5 to the combat DC, and caps it to one round. No effect for the social version of intimidate.

Cavall |
Well, there are traits that raise sense motive. That would have been the answer.
However sense motive doesn't factor into Intimidate.
The DC of this check is equal to 10 + the target’s Hit Dice + the target’s Wisdom modifier.
There are some class options as well that may help.
What class and race were you thinking of?
Obviously the most immediate answer is paladin. Being immune to fear means immune to shaken means immune to Intimidate.

Cavall |
Good news! Welcome to order of the cockatrice.
order of the cockatrice cavalier adds Appraise (Int) and Perform (Cha) to his list of class skills. In addition, an order of the cockatrice cavalier adds his Charisma modifier to the DC on another creature's attempt to demoralize him through Intimidate (in addition to his Wisdom modifier, as normal).

QuidEst |

Huh. Not sure why I thought it was either 10 + HD + wisdom, or 10 + Sense Motive bonus.
Class and race are set, and I don't think Cavalier or Kobold have anything special for that.
There's the Adopted trait, but you'd probably want to handwave away the "adopted" part if you did that.
You're thinking of combat bluff.

Avoron |
Sense motive factors into feinting, but not intimidate. That might have been what you were thinking of.
There are several traits that appear to do exactly what you're looking for.
Cynical Ear (social), DC to intimidate you or use diplomacy on you increases by 2
Free Spirit (social), DC to intimidate you increases by 2, plus you get a +1 to saves against language dependent or sonic effects.
Centered (religion, must worship Irori), DC to intimidate you increases by 1, plus you get a +1 to saves against charms and compulsions
Strong Heart (religion, must worship Gorum), DC to intimidate you increases by 2, plus you get a +1 to saves against fear
Fiery Dominance (regional, must have spent at least a year living in the plane of fire), DC for humanoids of a different subtype to intimidate you increases by 2, plus you get a +1 to Intimidate checks against such creatures.
Unflappable Arrogance (race, must be an Ifrit or get it through the Adopted social trait), DC to intimidate you increases by 5 and you cannot be demoralized for more than 1 round

Green Smashomancer |

Good news! Welcome to order of the cockatrice.
order of the cockatrice cavalier adds Appraise (Int) and Perform (Cha) to his list of class skills. In addition, an order of the cockatrice cavalier adds his Charisma modifier to the DC on another creature's attempt to demoralize him through Intimidate (in addition to his Wisdom modifier, as normal).
That's right, Cockatrice was on my list of Orders to choose from. I ended up going with Eastern Star for the save bonuses, so I don't perforate my allies down the road. I may reconsider it, though.
There's the Adopted trait, but you'd probably want to handwave away the "adopted" part if you did that.
You're thinking of combat bluff.
Actually, the Kobold is adopted. I might be able to use that.
List of ideas
It's too bad the only one of those that fits is Strong Heart, and the guys LG. Maybe it wouldn't be too weird for him to venerate Gorum.

Cavall |
Irori isn't a stretch for a LG. I could see a lot going for a kobold that was adopted and learned the ways of Irori because they saw value in him, a discipline others of his race may lack.
It could even have given him a self important attitude and make cockatrice still viable. But eastern star is decent as well, both are fun choices.

Avoron |
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It's too bad the only one of those that fits is Strong Heart, and the guys LG. Maybe it wouldn't be too weird for him to venerate Gorum.
Not that weird. The great thing about not being a divine caster is that you have lots of freedom with your religion and alignment.
This cavalier order exists to keep dangerous secrets hidden from the world and secretly protect the world against unimaginable threats from beyond the mortal realms. These cavaliers scout and observe, concerning themselves not with the trivial pursuit of morality, but rather with ensuring the survival of society itself.
Gorum is considered the divine embodiment of martial prowess, of glory on the battlefield, and it is believed that should conflicts like those that birthed the deity ever cease, he will perish as a result of their absence.
Lawful good characters are the crusaders of Golarion. Typically driven by religious zeal or a fervent sense of justice, these characters are often willing to take extreme personal risk to do what is right.