How do you define democracy?

Just taking countries that elected a government with universal adult suffrage, and a multi party system and with reasonably fair elections (i. e. the government was likely the same one who'd have won if the election was totally fair), there's been a few wars. The nature of these conflicts means that there likely wasn't a formal declaration of war, but that rarely happens now anyways.

Something akin to a conventional war took place with the Balkan states in the 1990s, and the onset of democracy could be seen as one of the causes.

In 1990, with the fall of communism, all of the Yugoslav Republics had had elections and voted for nationalist parties, and Slovenia, Croatia and Bosnia seceded, in that order. Serbia also voted nationalist, but it was in a politically dominant position in Yugoslavia, so Serbian nationalism took on the form of upholding the Yugoslav union. Serbia had a perfunctory war with Slovenia (there wasn't a large Serb population in Slovenia so Serbia didn't mind releasing the state, but they didn't want to set a precedent either), followed by a brutal three-way war between it, Bosnia and Croatia (and the autonomous militias of people that ended up in the 'wrong' state) , that ended when the Nato countries bombed Serbian (and Bosnian Serb) positions and forced a Croat-Bosnian alliance.

The Kosovan War was also fought between Nato and Serbia, with Nato aiding ethnic Albanian separatists in their attempt to secede, or at least regain their political autonomy.

The South Ossetian war of 2008 took place with Russia supporting separatists in a small region in the South Caucasus, against Georgia, in what the Russians portrayed as a mirror-image of the Kosovan precedent.

Edit: Wikipedia tells me this was accompanied by a formal declaration of war.

Israel has repeatedly invaded Lebanon over the years, with both governments being constitutionally elected, not without some issues on both sides.