I think it would depend upon what triggers the coup. OTL the conspirators were waiting for the west to show some backbone and support the czechs. Had they done so, and Hitler was couped in response, then appeasement is completely discredited, as clearly standing up to the bully causes them to collapse. Paul Reynaud, and his interventionist school of thought, will be completely vindicated. The little Entente is reinforced and reenvigourated, and any attempt to redraw the map of europe is jumped on by France, with Britain reluctantly following along.
At least for a while anyway. Democracies get bored with constantly being on alert, and governments change. So assuming Mussolini keeps his head down, which seems likely under the circumstances, and so does Stalin, which also seems likely, at least for a few years depending on how his support for the czechs has pacified his western borders, things should remain relatively calm in Europe while France play policeman. Until they grow tired of it again and their resolve weakens. At which point anything could happen. The Italians are stronger, but the Soviets will be a monster, and they may have rehabilitated their reputation enough to back the little Entente against Italy. I could see a war in the Balkans in the mid forties between a beefed up Italy and Hungary on the one side, and Yugoslavia,Czechloslovakia, and Rumania on the other, with the Little Entente winning due to massive Soviet aid. Possibly Germany seizes the opportunity to muscle Poland, and Stalin rediscovers the joys of pan slavism, and reaffirms the soviet western borders and supports them.
I do think that the likelihood of the new german government revisiting the sudetenland, the issue that caused the Heer to freak out and coup their government, anytime soon after 1938, to be very low. Or for that matter any revanchist issue. I mean really. " Hey, we're not hitler, and we got rid of him because he was going to get us into a war with the west, but let's start demanding the same stuff as him shall we, as clearly doing the same thing we were terrified of doing six months ago is a great idea now, and will go much better."
Yeah.....
Now if the Heer coups Hitler for even talking about the Sudetenland, ie. pre Munich, then the new german government is even less likely to revisit revanchism any time soon. Maybe the Italians get up to something in the Balkans, but without the cover of the Germans it won't be until they are ready by their own definition. Maybe 43 or 44, and by then any number of scenarios are plausible. Frankly, given Italy's long standing policy of trying to figure out who will win and then opportunistically joining that side, they may well keep their heads down for a while until an opportunity presents itself.