I've been commenting a lot and not answering for quite some time now! My hesitation was largely due to the terms "unfailingly", the mixture of "altruism" and "non-cruelty", and having forgotten my intention to answer. My answer certainly won't be foolproof (haven't yet heard of a trait model that is), and I may not cover both altruism and non-cruelty, but here are some pointers anyway...
To start this answer off "Big", I'll begin with agreeableness (and its Wikipedia page, which has a lot to offer on the topic), one of the Big Five personality traits [emphasis added throughout]:
Agreeableness is a personality trait manifesting itself in individual behavioral characteristics that are perceived as kind, sympathetic, cooperative, warm and considerate [(Thompson, 2008)].
All of these aspects (traits unto themselves, really) will relate somewhat to non-cruelty or altruism; even cooperation entails not harming one's teammates and sometimes putting them first.
People scoring low on agreeableness are generally less concerned with others' well-being and report having less empathy. Therefore, these individuals are less likely to go out of their way to help others. Low agreeableness is often characterized by skepticism about other people's motives, resulting in suspicion and unfriendliness. People very low on agreeableness have a tendency to be manipulative in their social relationships. They are also more likely to compete than to cooperate.
Less concern for others' well-being and emotions in general means greater freedom to disregard or willfully harm them, as are often useful to do for personal gain via manipulation or competition. Here we also have a direct connection to altruism, and a few indirect connections, including disinterest and mistrust of others' concerns. Yet the most direct connection to altruism appears in the facets of agreeableness (lower-order factors in a second-order model of agreeableness as a multidimensional construct; see Figure 1 for a similar model):
Agreeableness is considered to be a superordinate trait, meaning that it is a grouping of personality sub-traits that cluster together statistically. The lower-level traits, or facets, grouped under agreeableness are: trust, straightforwardness, altruism, compliance, modesty, and tender-mindedness [(Matsumoto & Juang, 2012)].
I've emphasized trust and straightforwardness above because the Big Five model of personality isn't the only one that relates trust to altruism—see also:
Figure 1. Second-order model of trust linking altruism to honesty (Perepelkin & Di Zhang, 2011).

Again, logically, a lack of trust would likely reduce motivation to help others altruistically. As for straightforwardness, Wikipedia notes, "Low scorers...are generally deceitful or manipulative." Again, these behaviors are likely to relate to some form of cruelty more often than not (i.e., "white lies" are the exception, I assume).
Also, from the same section, "Straightforwardness is similar to the honesty aspect of honesty-humility in the HEXACO model" (Ashton & Lee, 2005). So, speaking of HEXACO...
The factors of Agreeableness, Honesty-Humility and Emotionality are distinctly different from their counterparts on the Five Factor Model (FFM). Honesty-Humility, Emotionality and Agreeableness are proposed to be measures of Altruistic versus Antagonistic behaviour. Honesty-Humility and Agreeableness both measure two different aspects of Reciprocal altruism, high levels of which indicate a propensity for helping behaviour and cooperation as opposed to the exploitation of others. The Honesty-Humility factor represents a person's tendency for pro-social altruistic behaviours [(Thalmayer, Saucier, & Eigenhuis, 2011)], while Agreeableness indicates an individual's tendency to forgive and to show tolerance. Emotionality is a measure of kin altruism, that is, the tendency to show empathy and attachment to one’s kin.
This implies a little complexity in altruism itself, but brings agreeableness, honesty-humility, and emotionality directly into the equation within the HEXACO model. It may also claim that emotionality is "distinctly different" from neuroticism, but I'm not sure I'd go so far. Consider that neuroticism relates negatively to happiness in the context of the Wikipedia page on altruism itself:
While research supports the idea that altruistic acts bring about happiness, it has also been found to work in the opposite direction—that happier people are also kinder. The relationship between altruistic behavior and happiness is bidirectional. Studies have found that generosity increases linearly from sad to happy affective states [(Underwood, Froming, & Moore, 1977)]...While generous acts make people feel good about themselves, it is also important for people to appreciate the kindness they receive from others. Studies suggest that gratitude goes hand-in-hand with kindness and is also very important for our well-being. A study on the relationship happiness to various character strengths showed that "a conscious focus on gratitude led to reductions in negative affect and increases in optimistic appraisals, positive affect, offering emotional support, sleep quality, and well-being" [(Shimai, Otake, Park, Peterson, & Seligman, 2006).]
This adds happiness and gratitude to the equation as well, which can be measured at the trait level.
BTW, since empathy has come up a fair amount, you may be interested in the "empathy-altruism hypothesis". This also implicates empathy as a trait of sorts that relates to altruism, but I'm not sure this adds anything to what I've said above. Also, while I'm disclaiming, I may not have addressed cruelty sufficiently yet, much less neural correlates. Both are likely to make the necessary answer much bigger, so I'm at least going to take a break on this one for now. I'd encourage someone else to step up and cover those bases in the meantime.
References
- Ashton, M. C., & Lee, K. (2005). Honesty-Humility, the Big Five, and the Five-Factor Model. Journal of Personality, 73(5), 1321–1354.
- Matsumoto, D., & Juang, L. (2012). Culture and psychology (5th ed.), pp. 271. Belmont, CA: Wadsworth-Cengage Learning.
- Perepelkin, J., & Di Zhang, D. (2011). Brand personality and customer trust in community pharmacies. International Journal of Pharmaceutical and Healthcare Marketing, 5(3), 175–193.
-Post, S. G. (2005). Altruism, happiness, and health: It's good to be good. International Journal of Behavioral Medicine, 12(2), 66–77.
-Schwartz, C., Meisenhelder, J., Ma, Y., & Reed, G. (2003). Altruistic social interest behaviors are associated with better mental health. Psychosomatic Medicine, 65(5), 778–785.
-Shimai, S., Otake, K., Park, N., Peterson, C., & Seligman, M. P. (2006). Convergence of character strengths in American and Japanese young adults. Journal of Happiness Studies, 7(3), 311–322.
-Thalmayer, A. G., Saucier, G., & Eigenhuis, A. (2011). Comparative validity of brief to medium-length Big Five and Big Six Personality Questionnaires. Psychological Assessment, 23(4), 995–1009. Retrieved from http://pages.uoregon.edu/gsaucier/comp_val.pdf.
-Thompson, E. R. (2008). Development and validation of an international English big-five mini-markers. Personality and Individual Differences, 45(6), 542–548.
-Underwood, B., Froming, W. J., & Moore, B. S. (1977). Mood, attention, and altruism: A search for mediating variables. Developmental Psychology, 13(5), 541–542.