I go to school with Chinese exchange students that became very defensive when the history teacher described the Dalai Lama as "peaceful". They said he is a separatist that promotes violence against the Chinese and they even compared him to ISIL. I did a google search but was unable to find anything that showed the Dalai Lama promotes violence. Has the Dalai Lama ever promoted violence or terrorism against the Chinese?
On the question if the Dalai Lama has openly promoted violence against the Chinese probably not much material is to be found apart from dubious or partisan sources. However, it is acknowledged from all sides that people close to the Dalai Lama had close relations to the Tibetian guerilla, which has been supported covertly by the U.S. at that time to weaken the Communist government in China.
There is quite an extensive record of documents, including declassified U.S. government documents, about this covert C.I.A. support of the Tibetian uprisings in the 1950s, see https://en.wikipedia.org/wiki/CIA_Tibetan_program and the sources listed therein.
A good summary is the following L.A.Times article from 1998, which opens
For much of the 1960s, the CIA provided the Tibetan exile movement with $1.7 million a year for operations against China, including an annual subsidy of $180,000 for the Dalai Lama, according to newly released U.S. intelligence documents.
The money for the Tibetans and the Dalai Lama was part of the CIA's worldwide effort during the height of the Cold War to undermine Communist governments, particularly in the Soviet Union and China. In fact, the U.S. government committee that approved the Tibetan operations also authorized the disastrous Bay of Pigs invasion of Cuba.
It is questionable if the Dalai Lama at that time received financial support while at the same time not being knowledgeable about the support of guerilla training. In the article there are some further assertions by the Dalai Lama regarding this covert support, which has been initiated by his brothers (see also the obituaries for one of them in the NY Times and the Guardian):
In his 1990 autobiography, "Freedom in Exile," the Dalai Lama explained that his two brothers made contact with the CIA during a trip to India in 1956. The CIA agreed to help, "not because they cared about Tibetan independence, but as part of their worldwide efforts to destabilize all Communist governments," the Dalai Lama wrote.
"Naturally, my brothers judged it wise to keep this information from me. They knew what my reaction would have been."
The Dalai Lama also wrote regretfully in his book that the CIA had trained and equipped Tibetan guerrillas who conducted raids into Tibet from a base camp in Nepal.
The effect of these operations "only resulted in more suffering for the people of Tibet. Worse, these activities gave the Chinese government the opportunity to blame the efforts of those seeking to regain Tibetan independence on the activities of foreign powers--whereas, of course, it was an entirely Tibetan initiative."
Even if one accepts the Dalai Lamas's self-exoneration about his ignorance regarding the C.I.A. involvement then or assumes a change-of-mind, one can understand why the Chinese government still has significant reluctance to concede in further Tibetian autonomy claims.
Given the exhaustive history of open and covert regime change attempts of 'hostile governments' by the U.S., the Chinese government has good reasons to be extremely cautious by trying to delegitimize the Dalai Lama via their indoctrinal institutions in media and education.
Further information regarding the Tibetian uprisings in the 1959s can be found on the related Wikipedia article on the uprisings of 1959 and also in the articles of the special issue of the "Journal of Cold War Studies".
The present Dalai Lama is outspoken in his deep commitment to nonviolence. See, for example, this video on his website. It was even somewhat controversial when he made a statement in support of the UK's Armed Forces Day. But it does not appear that he has ever even vaguely suggested any support for armed struggle in the name of Tibetan independence.
However, that is not to say that all of the Dalai Lama's supporters are equally committed to nonviolence. For example, there was widespread civil unrest in Tibet during 2008. The Chinese government made claims (apparently baseless) that the Dalai Lama orchestrated the violence.