Sri Lanka with Sinhala and Tamizhar
Java containing sundanese and javanese
Vietnam consisting of chams and viet
Georgia and Armenia union
Lebanon that works out
Cyprus that works out
Nepal with Khas and Newars
The Tamil (Sri Lanka), Chams (Vietnam) and Newars (Nepal) are a small minority of their home countries, so they don't count. The Sundanese are about half as numerous as the Javanese, so that probably doesn't count either.
Lebanon works in terms of religion. A unified Georgia-Armenia would fit.
Cyprus currently wouldn't work - Greek Cypriots are about three times as numerous as Turkish Cypriots.
Remember, the OP specifies that the two groups should be roughly equal in size. Therefore, Czechoslovakia wouldn't count, since the Czechs were about twice as numerous as the Slovaks.
Denmark-Norway would work - Denmark has nearly 6 million people, whilst Norway has just over 5 million.
A country formed out of just Quebec and Ontario would also work - both provinces have approximately equal populations.
A timeline where the czech national revival is slowed and its identity weakened (but not entirely germanized) in the 19th century, that ends up with an Austria+Czechia?
The United Empire of France and Spain, commonly referred to as the Bourbon Empire.
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A timeline where the czech national revival is slowed and its identity weakened (but not entirely germanized) in the 19th century, that ends up with an Austria+Czechia
A surviving Austria-Hungary with just Austria and Hungary.
Bukovina had a significant number of Germans though. Maybe best for a former Austro-Hungarian Empire state would be Galicia where Poles and Ukrainians could play a balancing act.Alternatively, a surviving Austria-Hungary with neither Austria nor Hungary. My suggestion is Austria-Hungary gets reduced to a rump-state in Bukovina, which operates as a de facto bilingual Romanian and Ukrainian state, with Austrian German and Hungarian as official languages that almost nobody except court officials in the Imperial Court in Chernivtsi can speak.