Can the Cold War end with the Eastern bloc reforming their economies and avoiding the "Era of Stagnation" and without the Soviet Union collapsing afterwards?
Yes, it can.
It's hard though, since what was going on in the Satellites and Yugoslavia had a big influence on events in the USSR and vice versa. The Soviets being strong enough to survive but weak enough that they give up on Eastern Europe and allow it to liberalize (potentially extremely dangerous for them) requires things to happen just right. Further, no "Era of Stagnation" in the Eastern European Satellite states strengthens the USSR, both because the stagnation harmed the Soviet economy and world strategy and the debt-fueled boom that caused the E. European stagnation ALSO hurt the Soviets.
The "Era of Stagnation" in Eastern Europe involved paying for some poor choices in the 60s by the Eastern European regimes - namely, they all attempted debt-fed economic growth at the wrong time (since Western economies couldn't afford their exports due to the economic problems happening over in the West), meaning that instead of the money they borrowed from the West feeding economic growth, the borrowed money funded current consumption. This was just a huge mess of awful for the Eastern block - it weakened the Soviet system since Soviet citizens traveling to Eastern Europe lost faith in their own system, since they could see Eastern Europe "outperforming" them (and when those Soviet citizens included future decision-makers like Gorbachev, that was a problem); it made Eastern Europe dependent on the whims of the West, since defaulting on their loans would be humiliating - possibly to the point of endangering their regimes; it weakened Eastern Europe by masking the inefficiencies building up in their economies since in the short term they could stay inefficient and borrow more; it further weakened Eastern Europe because ultimately to meet those debts with long and brutal periods of austerity, which meant key services and needed investments weren't being made as the Satellite States (and Yugoslavia) struggled to pay back the loans of the 60s, which in turn weakened the legitimacy of the state far more than any other single factor.
And it's worth noting that just avoiding an austerity-generated stagnation doesn't involve avoiding
other stagnations. The Soviet stagnation going on at the same sort of time had different reasons (namely resource exhaustion in their Western territories combined with a huge expansion of oil production that allowed the Soviets to paper over the cracks and defer real reforms to their coal and steel industries). At the same time, countries like Algeria and Argentina were having similar periods of stagnation and crisis for their own reasons and even the much more robust and wealthy Western powers like the US and Britain were enduring their own periods of relative "stagnation" and crisis (of course, nowadays central bankers would kill for the growth rates that the Brezhev-era USSR had or the Nixon-era USA had) - witness the US coming off the gold standard, the death of ambition in the US Space Program and the British Winter of Discontent. Pretty much everyone had some sort of prolonged and traumatic economic crisis between 1970 and 1990.
So to get this exact outcome you want requires threading the eye of a needle.
fasquardon