We have to distinguish progress within philosophical moral theory as a field of study, and moral progress in society. There are many obvious examples of moral progress in society: the end of slavery, equal rights for various minority groups, greater concern for animal welfare, reduced exploitation of children, etc. While in many of these cases, moral philosophy played a role in the historical process of change what I take the question to be asking is whether we can say that moral philosophy itself has progressed as a field of study.
I think the answer is clearly yes. I specialized in moral philosophy in my graduate work in the early 2000s, I have not kept up with the academic literature since then. But looking at 20th century moral philosophy I'd say there are clear landmarks of progress in the field.
In 1903 Principia Ethica carved out morality/ethics as a field of study that was fundamentally distinct from both religion/theology on the one hand and psychology/social science on the other. Moore's famous naturalistic fallacy showed there was no easy way to derive a moral ought from a (non-moral) is. This made the field of moral philosophy an autonomous discipline. This could be compared to the way that Turing made computer science a discipline distinct from pure mathematics.
Another major landmark was Ross' The Right and the Good published in 1930 which in my opinion set up the bones of the current methodological framework of normative moral theory. A key idea was that there might be a plurality of fundamental moral principles rather than a single totalizing explanatory principle (as was the case with classical Kantianism, utilitarianism, and contractualism). Ross' work inspired subsequent generations of normative theorists to consider much more nuanced and complex types of theories than they had done previously.
It also enabled sub-specialization within the field. Today a moral theorist might say they specialize in working on theories of distributive justice or theories of human rights or theories of our duty to benefit others. The fact that each of these sub-areas of morality could be theorize separately is often take for granted today but that is a result of Ross' innovative idea of prima facie duties. There may never be one over-arching moral theory-of-everything.
The middle of the 20th century saw a bit of a retrograde motion away from normative theorizing and a focus on meta-ethics. This may have been due to the moral trauma of World War II (that's just my pet theory) as well as the preeminence in the 1950s America of various flavours of positivism and post-positivist naturalism. Morality suddenly didn't fit into the austere metaphysics that philosophers were enamored of. In some philosophical circles even to this day, there is much fretting and hand wringing about the "queerness" of moral metaphysics (to quote Mackie's famous descriptor which had nothing to do with LGBTQ issues). This continues to be a burden slowing or stopping the development of interesting normative theories.
However, just as most practicing mathematicians don't care a bit about the latest foundational developments in set theory, there have always been those philosophers who plunged ahead with normative theorizing without caring too much about meta-ethical quandaries. This itself is a sign of progress. When an academic field is too concerned with foundations, it usually prevents the development of substantive work on the actual content of the field.
This tendency to sideline meta-ethics in favour of normative questions exploded into the foreground with John Rawls' A Theory of Justice in the 1970s. While most of the book is about his particular theory of distributive justice, the biggest impact of this work on the field of moral philosophy may have been the chapters on methodology which introduced the methodological framework called reflective equilibrium. This made explicit, and offered a defense of what had tacitly been the modus operandi of moral philosophers. The use of our considered judgements about concrete moral cases as a sort of data against which to test our theories.
After Rawls there is a massive flourishing of the normative ethics. It's difficult to cherry pick individual examples of progress within such a broad Renaissance but I'd say one widely accepted example would be Derek Parfit's 1984 Reasons and Persons. In the intro, Parfit wrote: "Many introductions also try to explain how, when discussing morality, we can hope to make progress. Since the best explanation would be provided by making progress, this is the only explanation I shall try to give." Instead of doing a lot of inconclusive philosophizing about how it is possible to make progress in moral theory, he is saying let's just make some progress by actually doing a lot of compelling moral theory, and that will be an existence proof that progress is possible.
Many would agree that Reasons and Persons did make progress on a number of fronts. Besides the specific questions it addresses, its impact was to encourage a great deal more conceptual sophistication in moral argument. Parfit shows us that moral arguments (and the moral data of creatively imagined moral cases) can become extremely complex without ceasing to be intelligible.
However, here we also hit a bottle neck in the progress of moral philosophy. The level of sophistication that concepts and arguments normative theory have reached could not be sustained and further developed very far using the research paradigm of academic philosophy. Generally in philosophy one or two people work hard on a problem, shoving all the relevant ideas into their minds and coming up with something new. There is almost no emphasis on data collection and management or even working together on projects in large-scale teams. Kamm's 2006 Intricate Ethics pushes the Parfitian envelope even further with so many wildly complex thought experiments and proposed principles that many found it to be an impenetrable jungle. Perhaps such complexity could be managed were philosophers to leverage databases with structured knowledge representation technology but there is very limited institutional support for developing such systems.
In addition, the desiderata for career success in academic philosophy encourages divergent theorizing and objection raising over consensus building. A philosopher who merely builds on another philosopher's theory is seen as less original and will likely be less successful academically whereas finding an obscure and brilliant counter-example to a well regarded theory can often make one's whole career. It is not that the latter isn't valuable, but the incentives are weighted too heavily towards it. This incentive structure is markedly different from how things work in the sciences and social sciences where a large number of researchers are able to band together to form coherent research programs which are bigger than any individual thinker.
Perhaps normative ethics would have been better off if it had been able to split from philosophy to become it's own field of study, the way psychology did at the beginning of the 20th century. It still might end up going this way as the intricacy of the moral problems we face will only continue to increase through the 21st century.