Which suttas in the Pali Canon give flat out instructions for how to develop equanimity?
Also you can check out Sata,upekkha Sukha Sutta. (The happiness of pleasure and of equanimity.) A.2.7.9. When one is greedily attached to families one is always placed in an extreme position of difficulty and as a result one cannot maintain one's mental indifference, or equanimity. Equanimity (upekkha)is the main teaching of Buddhism. Attachment, either personal or impersonal, paves the way to ignorance (avijja) which prevents one from understanding what is good and evil, what is merit and what is demerit, what is right and what is wrong. Therefore we should be wise enough to be detached from the world as far as possible and of equanimity. But here I should emphatically say that revulsion is the other extreme. So attachment as well as revulsion should be understood very clearly and categorically. Understanding detachment paves the way to the realization of Nibbana through upekkha or equanimity.
MN 54 - Potaliya Sutta: To Potaliya
The Buddha said in the Potaliya Sutta of the Majjhima Nikaya that the pleasures of the senses are perilous and of much pain, (bahudukkha bahupayasa adinavo ettha bhiyyo). Seeing this with right discernment, as it actually is, then avoiding the equanimity coming from multiplicity, dependent on multiplicity, he develops the equanimity .
In this Sutta, pleasures have been compared to a skeleton (atthikankalupamakama), to a lump of flesh (mansa pesupama kama),to a grass torch made of straw (tinukkupama kama), to a pit of glowing embers (angarakasupamakama), to a dream (supinakupamakama), to what is borrowed (yacitakupamakama), and to the fruits of a tree (rukkha phalupamakama). Sensepleasures are normally of little satisfaction and of much pain. In the Alagaddupama Sutta of the Majjhima Nikaya the Buddha compared sensual pleasures; to a skeleton, a lump of meat, a torch of dried grass, a pit of glowing embers, a dream, something borrowed, the fruits of a tree, a slaughter house, an impaling stake, and a snake's head. There are ten comparisons. So we see that pleasures of the senses are through and through of little satisfaction and cause much tribulation. We shall now examine the relationship between raga and attachment.
In MN101 Buddha explains:
When I exert a fabrication against this cause of stress, then from the exertion of fabrication there is dispassion. When I look on with equanimity at that cause of stress, then from the development of equanimity there is dispassion.
What's meant here by fabrication, is a mental fabrication that counteracts the cause of stress. For example, when you see a person you like and suffer that you can never be together, you fabricate a thought like: "this person is actually not so good, we won't be happy together anyway" etc.
What's meant here by development of equanimity is looking at things philosophically and impersonally, as if from 30,000 miles away. You say to yourself, "this is just an instinct, the eyes caught the image, the brain interpreted it, the chemicals produced in the brain" etc.
Both of these techniques are further explained in the teaching on Five Perceptions (panca sanjna). The basic idea is that if dukkha is caused by a desire for an unobtainable attractive object, one should either fabricate perception of foulness, or perceive the object philosophically as a temporary arrangement of causes and conditions. And if dukkha is caused by repulsion for an unattractive object that one can't get rid of, one should either fabricate the attitude of metta, or again, perceive the object philosophically.
If you really think about it, the "philosophical" method is also a type of fabrication. We fabricate a perspective that sees the object under a different angle, which liberates the mind from the inner conflict that caused dukkha.
So what both methods boil down to, is understanding that all perspectives on things are optional, that you can pick any perspective you like, as long as it's helpful. The real equanimity comes from this realization that no perspective is "the right one" and from mastering an ability to switch perspectives at will, which leads to detachment from any single perspective and therefore to equanimity.