- The Operation Restore Hope point is a good one, and indeed there were sporadic exchanges of fire even in those early stages (mostly taken in their stride particularly by the USMC and the Belgian Para-Commando Regiment, who pointed out to the young clan-warfare guns involved why popping off rounds at two of the most professional groups of UN troops there was unwise.) And there were sporadic firefights and indeed UNOSOM casualties (lower than the ones they inflicted back but still casualties) over the course of UNOSOM I, which could be ranked a "lame-duck war" on a very small scale. It was Bubba's own damn fault displaying a Johnsonian desire to prove he would have a big swinging foreign policy that stuck around for UNOSOM II, so that one's entirely on him but UNOSOM I fits the bill.
- Johnson/Nixon -- there was already a low-grade guerilla war starting up along the Korean DMZ (indeed it carried on until about 1971, killed around a hundred GIs and probably a thousand or more North and South Koreans) which if added to the ongoing Pueblo crisis could easily have started Korean War II: Juche Boogaloo while Nixon was waiting to be sworn in.
- Ford/Carter -- two candidates here, both in Africa. Kissinger had a hard-on the size of Florida to "punish" Cuba for their interventions in Angola, Ethiopia, and elsewhere, and if some other country had turned towards the Eastern Bloc in that time he might have badgered Ford into a show-of-force blockade of Cuba that a series of advisors writing position papers on the idea pointed out could have been very dicey. Also, after the Entebbe raid in July 1976 Idi Amin ordered massacres of ethnic Kenyans over Kenya's collusion with the Israelis and Ford positioned the USS Ranger carrier group off the coast in response. And in late Feburary 1977, with Carter now in office, Amin "temporarily detained" a couple hundred American missionaries in Uganda for a few anxious days after Carter gave him an international tongue-lashing over human rights violations. Kludge some combination of those things together in the interim -- Kenyans dying by the hundreds or thousands, and Americans taken prisoner -- and Ford might Mayaguez him some foreign policy.
-Carter/Reagan -- There are stories, and there appears to be some corroboration, that besides designing a "Godzilla option" into the ten different mission profiles developed as part of Operation SNOWBIRD (the planning version of HONEY BADGER, the second plan for rescuing the Tehran Embassy hostages, one of which was the famous CREDIBLE SPORT with the rocket-boosted C-130s) that involved attacks on possible hostage hide sites around Tehran and northern Iran generally and on several other strategic targets in the country with a fairly large military force, Carter actually drafted a declaration of war against Iran as a last-resort option if they reneged on the Algiers Accords.
- Clinton/Bush -- Just make one of the Millenium attack plans work and make it messy. The Clinton administration had been infighting its way through almost attacking Afghanistan half a dozen times in the last couple of years of his presidency and that's probably all it would take. If they really wanted to drain the swamp that would carry on past the election, even unto the last hanging chad.
ETA: Given the provenance of the Bay of Pigs operation, and Eisenhower's advice to Kennedy during the Cuban Missile Crisis (one hopes Ike didn't truly understand that the Soviet nukes on site were fully operational when he counseled this) to party like it's June 6th 1944 with regard to Cuba, his administration might have ginned up a decapitating strike on the Castro regime at the end of 1959, when it had consolidated its power and showed it would lean towards Moscow but before the Soviets had gotten deeply involved providing aid. Indeed in some ways it's surprising they didn't (left to himself Nixon probably would've both to prove yes he was as tough on Moscow as Kennedy and to hand the new young president a problem to see if he was up to handling it.)
And, of course, like Eisenhower succeeding Truman, Obama when succeeding Dubya was handed pretty substantial military conflict, ongoing for sometime, and told "OK, buddy, you got elected, you fix it."