A Google Books Ngram view (Ѻ) of the use of the term "moral science", whose usage peaked between 1840 and 1875, falling into disuse in the 20th century.

“That branch of philosophy which, because it relates to manners, the Greeks usually term ethics [from: ήθος or ‘ethos’], the Latins have hitherto called the philosophy of manners. But it may be well for one who designs to enrich the Latin language, to call it moral science. And here we have to explain the nature and force of certain propositions which the Greeks term ‘axioms’. When these propositions relate to the future, and speak of possibilities and impossibilities, it is difficult to determine their precise force. Such propositions necessarily refer to the amount of possibility, and are only resolvable by logic, which I call the art of reasoning.”

“Philosophers in moral science have chosen to themselves a certain resplendent and illustrious mass of matter, to give glory either to the subtlety of their wit, or to the vigor of their eloquence. But such precepts as direct practice chiefly, (and life consists not in novelties or subtleties) they have for the most part omitted.”

The Wikipedia “moral science” page, which has been a redirect to “human science” since 2007, links to John Keynes, Alexander Bain, Stanley Jevons, George Magoun, Daniel Hausman, and to the talk page of “science of morality”, a discussion (Ѻ) on the difference between the two terms.

“Moral philosophy is nothing else but the science of what is good and evil, in the conversation, and society of mankind. Good and evil are names that signify our appetites, and aversions; which in different tempers, customs, and doctrines of men, are different: and diverse men, differ not only in their judgment, on the senses of what is pleasant and unpleasant to the taste, smell, hearing, touch, and sight; but also of what is conformable or disagreeable to reason, in the actions of common life.”

— Thomas Hobbes (1651), Leviathan [5]

“You are right in speaking of the moral foundations of science, but you cannot speak of the scientific foundations of morality.”

— Albert Einstein (1930), discussion on science and religion in Berlin [2]

“Even the greatest forces and abilities don’t seem to carry any clear instructions on how to use them. The sciences do not directly teach good or bad. Ethical values lie outside the scientific realm”

— Richard Feynman (1963), “A Scientist Looks at Society” [3]

“Science does not have a moral dimension. It is like a knife. If you give it to a surgeon or a murder, each will use it differently.”

— Wernher von Braun (c.1965), arose amid moral qualms surrounding WWII rocket science technology (Ѻ)

“The recurrence during the eighteenth century Enlightenment of the aspiration to be the ‘Newton of the moral sciences’ testifies to the prestige not just of celestial mechanics, but of the ‘experimental method’ more generally.”

— Stefan Collini (1993), ‘Introduction’ to C.P. Snow’s The Two Cultures [4]