I think I see what you're getting at with this question, but let me know if I've misunderstood - did the new historiography totally wipe the slate clean in late 16th- and 17th-century Ottoman history, or did are there aspects of the way Ottoman history was written in the older historiography which survive and are still relevant? The answer is that yes, there certainly are.

The question of whether the decline thesis had any positive aspects is a bit like the question of whether geocentric Ptolemaic astronomy had any positive aspects - those scholars did a lot of excellent work, but were limited by the available data and by the worldview inherent in the dominant paradigm. After the historiographical "revolution," all that old work didn't vanish, but it was repurposed and reimagined within the new interpretive framework.

So, for instance, scholars writing in the '50s and '60s would have characterized the decades following the death of Süleyman the Magnificent as one in which the sultan's personal authority over the state was weakening, disorder and banditry was spreading in the countryside, the empire's traditional institutional structure was breaking down, and military conquests were becoming increasingly difficult. All of these things were, indeed, actually happening. The sultans of the seventeenth century were for the most part less powerful than those of the sixteenth, public order in Anatolia did actually break down in the late sixteenth century with low-level banditry and sporadic rebellion continuing for decades, the empire's traditional institutions (particularly the timar system and devşirme) did deviate from their traditional function and eventually fell into abeyance, and with a handful of exceptions the Ottomans were no longer able to expand their borders after the mid-sixteenth century.

The difference lies in our interpretation why these things happened and what they should mean for Ottoman history as a whole. So to tackle the first point, we no longer find it necessary to equate the personal authority of the sultan with the strength and vitality of the state as a whole - weakening patrimonial authority allowed other groups to come to the fore and a more consultative form of government to emerge. Emphasizing the continuity and stability provided by the imperial bureaucracy, or the role of imperial women in helping the empire navigate periods of weak sultanic authority, or the ways in which the conditions of the seventeenth century could demand a different style of leadership than those of the sixteenth, has shifted our perspective away from a narrow focus on the sultan and onto a wider political arena. In other words, the declensionist historians were not wrong to say that the sultan's authority was weaker in later periods, but their limited focus on this and other issues led them to draw the wrong conclusions about the broader significance of the changes occurring in the empire.

Or in the case of banditry in Anatolia - prior to the work of Michael Cook and Mustafa Akdağ in the 1970s, the typical interpretation for the breakdown of order was to see it as a product of the failings of the Ottoman state. The Ottomans allowed their institutions to decay and corruption to spread, which ultimately produced endemic lawlessness. The above-mentioned scholars brought demographic factors into the picture, suggesting that Anatolia was suffering from population pressure following the sixteenth century's explosive population growth, while others (principally Halil İnalcık) put forth the argument that the Ottoman state was arming Anatolian peasants as musketeers in order to recruit them for its wars with the Habsburgs and Safavids, and that this was the primary cause of bandit activity. More recently, Sam White has emphasized the role of climatic downturn, suggesting that it was the so-called "Little Ice Age" which did the most to produce widespread rural misery and push peasants into banditry. So did rural order break down in the late sixteenth century, as earlier historians had claimed? Yes, absolutely. Was it simply because the Ottoman state was decaying? No. It was the result of a variety of factors, many of which were not under the Ottomans' control, others of which stemmed from efforts at problem-solving in other areas, as in the need to recruit an army of musketeers instead of the cavalry-based army that the traditional system was meant to produce. Perhaps most importantly, many of these conditions were not limited to the Ottoman empire. Similar conditions (e.g. population pressure and climatic downturn) are identifiable in many regions of Europe and Asia, as explored most recently in the book Global Crisis by Geoffrey Parker, making it problematic to see the challenges the Ottoman state faced during this period as something intrinsic to them alone.

As for modern proponents of the decline theory - there aren't, really. At least not among serious Ottomanists that I know of. I have never encountered any historian who has tried to put forward new arguments defending the decline thesis in its traditional formulation. It has simply been attacked from too many angles to make it a viable position to hold. Certainly, historians still disagree about plenty of aspects of the new presentation of Ottoman history, but nobody argues for trying to stuff the whole thing back in the box. Insofar as some have argued that the term "decline" still has some utility, they have used it in a much different way than it was understood in the 1950s.