I imagine the European Union probably might best fit this description, though I suspect that's not really what you're looking for.

The fundamental issue that keeps arising with entities that try for some sort of loose-knit confederacy is that they refuse to remain static. They either disintegrate (as in the US under the Articles of Confederation) or they experience a trend of greater centralization. In the nineteenth century, a number of states with "constitutions" similar to the Articles of Confederation had to be replaced with constitutions similar to the US Constitution. This was for much the same reasons as the US--the loose confederation model tended to create more problems then it solved, with perpetual disputes over sovereignty, taxation, and trade issues among others. One such was the Swiss Pact of 1815, which was replaced with the Swiss Constitution of 1848. Another was the Australian Constitution of 1900, which supplanted the confederal system established under the British in 1885. In the twentieth century as well, loose-knit, confederal arrangements seem to exist mostly in transitory periods, and seem to give rise to ultimately more centralized systems.

For example, the Russian Federation (I'm using it's formal name to emphasize its federal, though still highly centralized, nature) is comprised of various distinct political units. These units have experienced oscillating levels of control from Russia. Some have long experienced Russian control, yet still view themselves as possessing distinct identities. They have utilized periods of unrest (like the Bolshevik Revolution and the collapse of the Soviet Union) to renegotiate their status. One such is the Republic of Tartarstan, which was unsuccessful in its independence bid during the Bolshevik Revolution, but post-1992 has managed to carve out greater political space for itself relative to most other republics. Another is the Republic of Tuva, which still has the right of secession in its constitution--a result of its original precondition to join the USSR in 1944. Of course, the Russian Federation is still a highly centralized state. Nonetheless, its at these periods of internal instability--transitory periods--that such political units attempted to renegotiate sovereignty.

Similarly, the Chinese state presides over several distinctly identifiable political units. Like Russia, it is currently a highly centralized state (though it is a unitary state, rather than a federation). But also like Russia, periods of internal instability have seen renegotiation over status. In their fight against the Nationalists, the Communists attempted to specifically win-over distinctly identifiable minorities at least as far back as 1923 with the advent of "Minority Ethnic Cadres." The Party recognized some minorities as "nationalities" and promised self-determination or republic status in a future federal-type configuration. However, by 1953 the Party had abandoned such terminology, replacing "self-determination" with "autonomy" and "republic" status with "region." The takeaway is this transitory period from 1911 to around 1960 saw the status of distinct political regions within modern China fluctuate drastically. (Anything prior to 1911 would be difficult to classify using the concept of the nation-state system, as China was an empire with somewhat unique and still contested relationships with these political units).

Sources:

Nicholas Aroney, "Formation, Representation and Amendment in Federal Constitutions," American Journal of Comparative Law, 54:1, December 2006; University of Queensland TC Beirne School of Law Research Paper No. 07-10.

Alla A Yaz'kova, "Russia and Its Minorities: An Overview of Existing and Potential Ethno-political Conflicts," Innovation 19:3-4, 2006.

Regina Goodnow and Robert Moser, “Layers of Ethnicity: The Effects of Ethnic Federalism, Majority- Minority Districts, and Minority Concentration on the Electoral Success of Ethnic Minorities in Russia.” Comparative Political Studies, 45:167, 2012.

Xia Chunli, “To Be Masters of Their Own Affairs: Minorities’ Representation and Regional Autonomy in the People’s Republic of China.” Asia-Pacific Journal of Law and Human Rights, 1:24-46, 2007.

Yash Ghai, “Autonomy Regimes in China: Coping with Ethnic and Economic Diversity.” Autonomy and Ethnicity: Negotiationg Competing Claims in Multi-Ethnic States. Ed. Yash Ghai, 2000.

Other than the United States under the Articles of Confederation, the only two I can think of are of course the Confederate States of America (which probably wouldn't even qualify under the definition you are putting forth) and the Confederation of the Rhine set up by Napoleon in 1806 following the dissolution of the Holy Roman Empire. Neither lasted a decade.

There of course may be more (especially prior to these since the rise of the modern nation state did not occur until after Napoleon), but I am personally unaware of them. I do like this question though. Hopefully you get more detailed answers from someone who knows more history than I do.

The ancient Greeks constantly formed leagues and federations, only to reform and reconstitute. The Boiotian League was one of the most enduring, where each polis contributed a number of representatives to a governing council. While Thebes was the dominant polis, each city had its own council which ratified decisions from the federal council.