What innovations in ethics occurred within Christendom during the 9th Century? I am looking for any noteworthy developments, formulations, or codifications of ethics that occurred between 770 and 890 AD in any country or empire that was nominally Christian. If the answer relates to Charlemagne, even better. Who were the theologians, legal scholars, noblemen, rulers, or clergy that put forth these ideas or enacted them in law or custom?

If you know of several, which would you say had the longest lasting influence?

The ideas need not be specifically related to Christian theology; they only need to be informed by such a worldview. In a different epoch, an answer might include the Code of Justinian or the Magna Carta.

Research note:

I just came across a wonderful resource: https://historyofphilosophy.net/
It has podcasts from Kings College in London on a wide range of topics, including several about the Carolingian Renaissance and John Scotus Eriugna.
What innovations in ethics occurred within Christendom during the 9th Century? 

To start with, Charlemagne banned work on Sundays in 789. 


  In the West, Emperor Charlemagne in 789 banned work on Sunday as a violation of the third commandment of God. In 1234, under Pope Gregory ІХ, the law of Sunday rest became a universal practice in the Latin Church. - The History of Sunday Observance


Charlemagne once elevated to the dignity of Holy Roman Emperor, imposed Gregorian Chant as the norm for ecclesiastical chant throughout his kingdom.

At his request, Pope Hadrian I sent monks from Rome to the court of Aachen to instruct his chapel's choir in 774. This event helped spark the spread of traditional Gregorian chant through the Frankish churches. In 789, Charlemagne also issued a decree to his empire's clergy, instructing them to learn (and sing properly) the Cantus Romanus, or Roman chant. Music schools were also founded under Charlemagne's reign, and monks transcribing music helped preserve the Gregorian chant into the present day.


  Scholars debate whether the essentials of the melodies originated in Rome, before the 7th century, or in Francia, in the 8th and early 9th centuries. Traditionalists point to evidence supporting an important role for Pope Gregory the Great between 590 and 604, such as that presented in H. Bewerung's article in the Catholic Encyclopedia. Scholarly consensus, supported by Willi Apel and Robert Snow, asserts instead that Gregorian chant developed around 750 from a synthesis of Roman and Gallican chant commissioned by Carolingian rulers in France. During a visit to Gaul in 752-753, Pope Stephen II had celebrated Mass using Roman chant. According to Charlemagne, his father Pepin abolished the local Gallican rites in favour of the Roman use, in order to strengthen ties with Rome. In 785-786, at Charlemagne's request, Pope Hadrian I sent a papal sacramentary with Roman chants to the Carolingian court. This Roman chant was subsequently modified, influenced by local styles and Gallican chant, and later adapted into the system of eight modes. This Frankish-Roman Carolingian chant, augmented with new chants to complete the liturgical year, became known as "Gregorian." Originally the chant was probably so named to honour the contemporary Pope Gregory II, but later lore attributed the authorship of chant to his more famous predecessor Gregory the Great. Gregory was portrayed dictating plainchant inspired by a dove representing the Holy Spirit, giving Gregorian chant the stamp of holy authority. The myth of Gregory's authorship is popularly accepted as fact to this day.
  
  Gregorian chant appeared in a remarkably uniform state across Europe within a short time. Charlemagne, once elevated to Holy Roman Emperor, aggressively spread Gregorian chant throughout his empire to consolidate religious and secular power, requiring the clergy to use the new repertory on pain of death. From English and German sources, Gregorian chant spread north to Scandinavia, Iceland and Finland. In 885, Pope Stephen V banned the Slavonic liturgy, leading to the ascendancy of Gregorian chant in Eastern Catholic lands including Poland, Moravia, Slovakia, and Austria. - Gregorian chant


Charlemagne made reforms within the Church:


  Unlike his father, Pepin, and uncle Carloman, Charlemagne expanded the reform program of the church. The deepening of the spiritual life was later to be seen as central to public policy and royal governance. His reform focused on the strengthening of the church’s power structure, advancing the skill and moral quality of the clergy, standardizing liturgical practices, improving on the basic tenets of the faith and moral, and rooting out paganism. His authority was now extended over church and state; he could discipline clerics, control ecclesiastical property, and define orthodox doctrine. Despite the harsh legislation and sudden change, he had grown a well-developed support from the clergy who approved his desire to deepen the piety and morals of his Christian subjects. - Church Reform


Charlemagne standardize silver currency in his day.

As Charlemagne conquered Western Europe, he recognized the need for a standard currency. Instead of a variety of different gold coins, his government produced and disseminated silver coinage that could be traded across the empire—the first common currency on the continent since the Roman era. The currency’s system of dividing a Carolingian pound of pure silver into 240 pieces was so successful that France kept a basic version of it until the French Revolution.


  Europe was entering its fourth century of the "Dark Ages" when Charlemagne was born in A.D. 742, a time marked by frequent warfare, few important cultural achievements and the virtual cessation of learning. Charlemagne became ruler of one of those kingdoms in Germany in A.D. 768 and immediately set about expanding his territory. Through the course of more than 50 battles, most of which he led in person, he'd conquered almost all of mainland Europe. Everywhere his rule was established, Charlemagne instituted the same reforms, creating a common identity in people from eastern Germany to southern Spain. Commerce boomed. One of the most important changes Charlemagne made was abandoning the gold standard and putting all of Europe on the same silver currency. Trade became easier and the continent prospered, aided by laws that took some power away from the nobles and let the peasantry participate in commerce. The lower classes benefited in other ways under Charlemagne, who was frustrated with the nobility's sense of entitlement and had deep sympathy for the peasants, according to historians. Among other legislation, all local regional governors were subject to regular inspections by royal emissaries to make sure no injustices were being done. Educational reform was also high on Charlemagne's agenda. The progressive leader loved to learn, historians say, and so encouraged schooling throughout his kingdom in his chosen lingua franca, Latin. - How Charlemagne Changed the World


More information may be gleaned from the following articles:


Early Medieval Ethics
Alcuin (Catholic Encyclopedia): An eminent educator, scholar, and theologian born about 735; died 19 May, 804. He came of noble Northumbrian parentage. While returning from Rome in March, 781, he met Charlemagne at Parma, and was induced by that prince, whom he greatly admired, to remove to France and take up residence at the royal court as "Master of the Palace School".