Nationalism can be a strong cohesive force to unify a country; and can stabilize it substantially. There were strong outbursts of nationalism in the United States after the attack on Pearl Harbor and again on September 11, 2001. Partisan differences are often forgotten. Japan to this day is a strongly nationalist country, and although it has some economic difficulties, there is no sign of instability. Still, Nationalism is like fire--it can be useful but too much can be dangerous. One only need consider the example of National Socialist Germany to understand this. The end result was the total destruction of the government and military occupation of the country. So one might argue that it is destabilizing to the extent that it leads to aggression which in turn will cause a defensive--if not offensive--reaction from other countries.
I think if you look at Nationalism as how it relates to the stabilization within the country, it does stabilize it. It promotes community and cooperation all for one cause. However as mentioned above while it may stabilize your own country it could also work to destabilize your relationships with other countries.
Nationalism can be both a stabilizing or a destabilizing force, depending on the circumstances in which it arises and the degree to which it exists.
A mild version of nationalism, especially in a country where the vast majority of people share in the nationalism, can be stabilizing. For example, China seems to be getting more nationalistic. The people of China are becoming prouder of their country because of its growing economic power. This acts to stabilize the country of China because it makes the people happier to be part of that country and less likely to be angry at their government.
A more aggressive nationalism can be destabilizing, especially to the international community. For example, Iranian nationalism can be seen as destabilizing the Middle East. As Iran becomes more nationalistic and tries to gain more power, it starts to worry the countries around it. This is especially true since Iran is a Persian country whereas the countries around it are Arab. This would mean that Iranian nationalism might be antagonistic towards its neighbors.
So nationalism can stabilize or destabilize a country or region, depending on the circumstances.