Warfare in democracy is not impossible to maintain if you are attacked, and your peoples luxuries are met, and your forces aren't in enemy territory. I just fought a lengthy (guessing 70 year) war w/ the Americans.
I, too, hate the AI method of dumping a stack of units in your territory and declaring war. I *know* this is the AI tactic, so I had my border w/ them cluttered with fortresses defended by MechInf such that there was no way they could strike my cities on their first assualt (they had to spend their MP's, but could not attack).
edit: They did have ~10 armor too (which is odd, in itself for the AI), but for some reason, they did not move to the adjacent city square (which, considering AI tactics, might not be so odd).
So, here is ~90 US MechInf in my territory, and one square away from Antioch. I summoned workers to surround the stack, build fortresses, and fortified w/ MechInf. I had a reserve of 50 cruise missles, so I used them. It took several turns of maneuver, but I kept the US force in my territory, and away from Antioch. For the cost of a few of my MechInf in the fortresses, and 50+ missiles, I destroyed their entire invasion force.
The kicker was I got 2 allies to declare war on US, signed ROP, and let them stream through my territory to US. Then I blocked both allies land routes through my territory, and let the allies and US bleed each other out. By then, my cruise missile inventory had been restocked.
I use missiles as bombardment (arty is useless - missiles can KILL enemy units). So, I send missile after missile against city, until last defender is dead. Send in MechInf - city is mine, and my units have never left my territory. Rinse, repeat as necessary.
Oh, and my 15 armies of armor was of some benefit, too.
A little slower than some of you may want, but I only have to produce cruise missiles. My core cities were tossing out CM's every 1 or 2 turns. I never lost an army, only a couple of solo armor.