They burn themselves because, from the age of five onwards, they go to school in monasteries. In them, these children are trained to be ascetic monks in the middle of the most materialistic society on Earth. When they graduate, they can't find gainful employment because they haven't learned anything except how to chant prayers and shout slogans and worship, in secret, a very human and very fallible exile. Then they go back to the monastery and spend all day being useless, and one day they grow frustrated (in more ways than one) and go find some kerosene and a match.
The solution? Sinify and secularize the children. All of them.
Bar Tibetan parents from enrolling any children in these monasteries, enforce compulsory public education in secular schools, and bar religiously-oriented individuals from teaching in or even working as janitors or staff in the schools--basically, a zealous interpretation of the American First Amendment. Test the kids yearly; at age ten, put the smartest 1% in strictly secular boarding schools to get these kids away from any and all religious influences. For the rest of the children, encourage them to attend vocational schools post-graduation that let them become the builders of a better tomorrow for China and Tibet.
Give the 1% scholarships to attend colleges on the wealthy east coast of China, pick up useful skills like engineering, medicine, and law, and work on the wealthy East Coast of China, far away from Tibet. Keep soft tabs on them and encourage them to marry into Chinese society. Isolated from the family unit, these kids will search for a sense of belonging--so offer membership into the Communist Youth League, but make it selective and exclusive to the best of the best, so that all the brightest ethnic Tibetans compete against each other for acceptance into the Chinese party-state.
There are only ten million ethnic Tibetans, so every year this program would have to encompass about 100,000 to 200,000 children--a 1% cutoff is 1,000-2,000 kids, which means the program is doable with the right amount of funding. Indeed, this could be dressed up as a charity--set up a foundation to promote education in Tibet, base it out of Hong Kong, make its finances (but not its operations) transparent to the Western media, and hell, you could even tap into the very same Western foundations that salivate at the thought of splitting apart China into helping you completely Sinify the best and brightest Tibetan youth, year after year, decade after decade, until these Tibetans identify more with Beijing than Dharamsala, and can be reliably counted upon to govern out of Lhasa.
Eventually, the problem will go away. And heck--every time Tibetans attack one of these schools, incite the Tibetans to violence and try to get them to shoot at the schools. Then you can put egg on the face of the Tibetan movement in the West, by making them look like the same Taliban religious zealots shooting up schools in Pakistan and Afghanistan.