It is a quality of people to say that it is very active (being a diligent person). In Christianity, the Stagecoach is considered one of the cardinal virtues (cardinal Word applies here in the sense of direction, i.e. serving as address or guide the faithful). Opposed to laziness (one of the deadly sins) and Latin 'diligere' has the meaning of love among other translations. Santa Teresita del Niño Jesús said that if one together with love (diligence) to God a pin the fact was so powerful as a great mission among people who did not believe.
In this sense do something with diligence means doing so with care and love, i.e. with the heart in what you do. Many times one does things with care, I remember an English teacher who put a great dedication in what he was doing but always complained that that was not theirs (young wanted to be an architect) and I asked him about how many of their students had failed the baccalaureate tests in the last 10 years (I know the answer): none told me. I said "If that is not your thing I do not understand what what you complain". I think that until that day he realized that he loved teaching, which we happen to many with our professions, but came through the pores without doubt by the diligent that is.
Let me clarify that also was called 'diligence' a type of carriage pulled by horses that was widely used in the Western United States, Australia and some other countries to transport people, goods and money. It was built very strong wood and with several compartments (there were several models) Although the most used was of a single compartment. They were the main form of communication in remote areas since they were also carrying the mail. Many companies, mostly associated with banks kept them because he was the safe way to transport values where not reached the railway routes and schedules quite strict.