Normally in Buddhism we don't "tolerate" negative emotions. We tolerate negative experiences, but negative emotions is something we would like to eliminate.
Joyfulness and positive emotions is something we are taught to generate, starting from coarse and then progressively finer, until we arrive at pure suchness, which is not an emotion at all.
Generally speaking, negative emotions arise due to all kinds of (mental/emotional) attachments. A standard technique probably taught by all schools is to see attachment/preconception/overgeneralization behind the emotion and to let that go. If emotion is particularly strong it may help to first learn to localize it as psychosomatic experience somewhere around the body image, and to reduce it with psychosomatic methods (breathing, moving, relaxation, visualizations). Some teachers suggest massaging or tickling the air in the area where emotion is felt, or tapping the body at that spot. In any case, psychosomatic methods are secondary. The primary technique is to learn to pacify the inner conflicts through control of conceptual fabrications. I've heard many descriptions of this: learning to construct wholesome narratives, learning to switch perspectives at will etc. but they all boil down to the same principle: tapping into brain's evaluation mechanism.
The same principle is at work for generating positive emotions. The basic skill is to control one's perspectives and the personal narratives that come from it. It is the same technique most people unconsciously use to maintain their ego: finding reasons to congratulate oneself, and reinvesting the joy that comes from that into further effort in the same direction. The only difference here is that Buddhists use it consistently with Ethics, and with perfect awareness of Emptiness, so they don't get lost in their own fabrications and don't create unwholesome results.
To boil this down to one principle: it is all about "The Given" and "The Ought" or simply "Is" and "Should". A mismatch leads to negative emotions, a match leads to positive emotions. Everything we do in Buddhism, regardless of how a particular school presents it, serves only one goal: to minimize the mismatch, to fabricate a match, and to eventually transcend the dichotomy altogether.