Ah yes, this will be a longer one.
First of, we actually have a rather excellent POD for this to happen, the August 38 travel of certain Ewald von Kleist-Schmenzin, a prussian arristocrat, long-term opponent of the Nazi regime, send by general Beck ad Carl Goerdeler to find out the British possition (the travel was financed by Admiral Canaris himself). He met with Churchill, and actually mananged to get both him and lord Halifax on the good side of the German opposition. When they later tried to get Chamberlein's support, he made unfavourable comparisons between the German opposition and the Jacobites of old. Aside from a few inconclusive meetings between Halifax and other members of the opposition, this was mostly it. Chamberlein deciding to take this opposition seriously, as a dagger aimed at Reich's heart, and hold a firm line against the Nazi's, would be the change needed.
Now, even a British declaration of support is unlikely to change Hitler's timetable too much, the 28. of September likely remains the invasion date, with diplomatic plays, the Sudeten uprising, the seizure of Aš by the SS and other such happenings still occuring, though with the major change that Britain would not push for Czechoslovak declarations of being willing to sacrifice territory (no Godesberg and such). Indeed, there will likely be an earlier push for Czechoslovak mobillization, with Prague happy to oblige. In the end there are two main variants here, starting on the 28.:
The Coup:
The fact that a conspiracy was ready to go is clear without any doubts. At least officially the plan was rather simple. Upon a declaration of war, a unit of 50 would seize Hitler, drive him to a well known psychiatrist who would then declare him insane. Leading nazi members would be arrested, while loyal army units under Höpner would fully secure the city. With the pro-nazi generals on the CS border (such as Reichenau), they would have little chance to actively join on either side,especially with coup-sympathizers present in their armies. SS and party officials would be arrested over the country, with the aid of pro-coup forces all over it. They would put together a somewhat broad government, give a crown to Willhelm II's grandson to have a uniting figure, and all would live happily ever after.
Alright, now to the issues. For one, the Hitler part. Several of those that were supposed to arrest Hitler, hhad already decided beforehand that killing the screeching bastard would be much more effective. Which might well have the effect of galvanizing the NSDAP loyalists. The plans to arrest many of the leading party members, especially outside Berlin, were often iffy, and there was even a large group that wished to cooperate with Göring and others. While coup loyal units were near Berlin, so was the 1. SS division under Sepp Dietrich, who would be quite certain to make a move against the coup. The support of Abwehr would be essential here (which considering the involvement of Canaris and Hans Oster was quite probable).
All in all, it is quite possible that a swift coup could easily devolve into a full civil war. Local Gaulaiters, army units, SS members, and who knows how the armies stationed against CS would react. Still, any threat against Prague, Paris or London would be neutralized for the moment, in either outcome. Germany would be weakened, and even if the pro-Nezi side won, it would likely be under somewhat pragmatic people like Göring. So still evil, but hopefully not world-domination/kill all non-Aryans evil. How long such a regime would last is unknowable.
But, best laid plans of Mice and Morons. All can fail, the conspirators might chicken out, or get purged. So option 2:
The War
All right, imagine if you will running into a wall. After a few tries, you manage to break through, only to find another wall. And then another. And so-on. Untill suddenly you get hit by a fist that breaks your nose. That would be the likeliest state of the German-CS war. Wehrmacht slowly grinding itself against a series of deffensive lines, mostly manned by 2. rate mobillzed troops, while the main part of CS army is waiting to start a general battle, and jump the Germans with several hundred tanks and large amount of fresh and trained men.
Even if the Germans do manage to take Prague in a month or two, they now have to continue fighting all the way to Slovak borders, and hope that at this point the CS army finally gives up. If they don't, welcome to Slovakia! Even more mountains and possitions to deffend, while the gold and sources you were looking to seize have already crossed to Romania. Oh, and its winter.
Meanwhile, Germany can't even use its full stregth, with one army on Sigfried, pissing its pants in fear of French army actually moving, another one in East Prussia against either Poland or USSR, all the while the German trade gets blockaded by the British fleet, and half the airforce has to be kept in reserve against French or British strike. At the same time, Mussolini is smiling at Hitler, saying that he will certainly help, in a few years, while Horthy has the whole Romanian army at his borders, waiting to be given an excuse to take Budapest again. The Poles meanwhile are considering if taking a few bits of Germany wouldn't be better then the relatively small rewards they get in Czechoslovakia, and the German people are beginning to loose all the enthusiasm, angered by getting dragged into another long, bloody and seemingly pointless conflict.
Any war in Czechoslovakia would not be comparable to the invasion of Poland. The geography, the army strength and doctrine, and other factors, would mean at least 3 months of brutall fighting, with an uncertain victor. 48 to 42 divissions was the strength divide. The German tanks and artillery might e more numerous, but are inferior in quality, and likely to face problems with ammunition. The airforce is Germany's main advantage, and a large part of it will have to be stationed in the West, if only as detterence. And even if the September conspiracy doesn't act, a few months of barely advancing will likely materialize a new one.
