What if the coup d'etat in 1941 failed. Let's say one of the leaders died in some sort of an accident and the coup wasn't done properly or if someone betrayed them leading to the arrest of the plotters. What would the consequences be?
1. Would Yugoslavia stay in the Tripartite Pact? The Germans would probably manage to find a way in the deal to move their army through to Greece and then later, since many of the neighbours wanted Yugoslav territory, they could at least strong-arm them to give up most of Dalmatia and some islands to Italy in exchange for a part of Greek Macedonia, of course if the Royal Yugoslav Army contributes to the campaign.
2. Would they help Germany in any other operations? At least they could get some volunteers like the OTL SS Prinz Eugen Division. Anything else?
3. Would there be much resistance in Yugoslavia? In 1939 Banovina Croatia was created and was supposed to give them some autonomy although it lasted shortly and there's not much to it. There was a lot of ethnic tension and the communists under Tito are sure to start a resistance as soon Barbarossa begins. Probably there would be no chetnik movement and Yugoslavia would have to open up some concentration camps and deport Jews and Roma to Poland or somewhere. Maybe the communists would have more support than OTL as the ustaša movement would be butterflied away if Yugoslavia has to survive. But surely a stronger Yugoslav army with the help of some German divisions and the Luftwaffe could defeat them...they survived barely OTL anyway. If Tito and the rest of the leaders are taken out or if they get surrounded like on Neretva or Sutjeska and their main army is destroyed the partisan movement would be severely weakened.
4. With no invasion of Yugoslavia Barbarossa could start earlier. Not much, maybe a week, but how much would that have effect on the Eastern Front. The Germans are still going to lose, but also, if the partisans in Yugoslavia are "mostly" dealt with by the end of 1942, that could free up some German and Italian troops that could fight in Ukraine against the Red Army or on Sicily in Operation Husky. It would be small changes but how much. Could the Soviet counterinvasion be slowed down, at least by a couple weeks, allowing the Wallies more success in Central Europe?
5. If Yugoslavia like this survives until 1944 when Germany is badly losing on all fronts, what would happen next? By now king Peter would rule without a regency, but definitely he couldn't stay on the throne, not without massive help from the west. The Americans themselves said they wouldn't help Yugoslavia in any peace talks if they join Germany. Could it become a democracy? Could the Soviets take Yugoslavia under their control? Maybe a coup? What are the possibilites?