What personality traits affect ability to cope with pain?
Gathered from M. Pecina et al., “Personality Trait Predictors of Placebo Analgesia and Neurobiological Correlates,” Neuropsychopharmacology, doi: 10.1038/NPP.2012.227, 2012:


  A recent study has found that personality traits appear to influence
  how strongly a person responds to a placebo treatment for pain.


http://www.psychologytoday.com/blog/unique-everybody-else/201301/personality-and-pain-relief


  Pain relief tended to be stronger in participants who rated themselves
  higher in the personality traits of ego resiliency and agreeableness
  and lower in neuroticism.
  [...]
  The facets that predicted placebo response most strongly were high altruism and straightforwardness (facets of agreeableness) and low angry hostility (a neuroticism facet that is also related to low agreeableness).


More thorough explanations are found in the link provided.
Further information on the same study:
http://www.the-scientist.com/?articles.view/articleNo/33300/title/Personality-Predicts-Placebo-Effect/