The 1982 Falkands War arguably is a case in point. Of course, the cassus belli wasn't officially "we want to distract our own folks", but it did have that rather convenient side-effect.

Argentina had seen President Peron overthrown by a military Junta in 1976. Galtieri took over from Viola in December 1981.

Galtieri had two problems. Firstly, a condition of support for his rule from some members of the military (Malvinists) was that the Malvinas (Falkland Islands to most of us) be returned to Argentine sovereignty. They were happy enough to do it diplomatically, the use of force was a back-up if the negotiations didn't seem likely to succeed. It may not have been absolutely critical, the head of the Navy (Anaya) was a friend and supporter of Galtieri in any case, but it did help Galtieri's position. Shortly after taking over, Galtieri announced that 1982 would be the Year of the Malvinas.

The other problem was more large scale domestic. To quote Martin Middlebrook: Galtieri and his colleagues were in difficulties. The Argentinian situation in early 1982 has been described many times: Falling industrial output, falling wages, rising unemployment, a massive inflation of well over 100% and still climbing. [...] the mass of the population were becoming desperate. The military had been able to establish a political stability of sorts, but only by the use of savage repression against those who opposed the regime. [...] General Galtieri and his colleagues needed a diversion and the one issue which united all Argentinians was that of the Malvinas

I'm honestly not entirely sure what the plan was for the country's inflation, unemployment etc problems once the Malvinas were secured, but it certainly had the desired effect, at least for a couple of months. The thousands of people on the streets on 2 April 1982 were, for once, not protesting the government, but cheering in celebration.