Thank you all for lending your thoughts and insights into this question. After reading through the answers and studying this matter a little more, my personal take-away is thoughtless (as possibly Jacob was in giving Joseph the special coat) or cruel favoritism (a common theme in many stories and accounts of abusive parenting) in gift giving to one’s children can indeed be sinful when it provokes children’s sense of fairness and tempts the victim as well as the “favored” into the near occasion of several sins (greed, envy, anger for the gift but as well as for a parent’s love).
To help avoid such outcomes, it becomes important for the parent to practice “reasonable” fairness in gift-giving. And when gift giving can’t (or shouldn’t) be “equal”, a well founded reason should be provided to ensure that all parties can understand why, for example, Joseph received the colored coat.
Also in gift giving we can turn our eyes to the story of the prodigal son whose loving Father gave him an equal share though, clearly, he was not equal in virtue to his brother.
If gift giving to one’s children does indeed require careful consideration to avoid provocation, then, like other parental activities, it is subject to the following calls from our Church (from the Catechism):
2222 Parents must regard their children as children of God and respect them as human persons.
2223 Parents have a grave responsibility to give good example to their children.
2287 Anyone who uses the power at his disposal in such a way that it leads others to do wrong becomes guilty of scandal and responsible for the evil that he has directly or indirectly encouraged. “Temptations to sin are sure to come; but woe to him by whom they come!”