Most courses on Coursera tend towards the technical or quantative (maths, science, engineering, etc). I imagine this is partly because arts courses, with their writing based assessments, are harder to grade online and the marking system doesn’t scale well. However, there are a few around. I just finished The Ancient Greeks course from Wesleyan University.
Notably this course does not contain any written assignments – all assessment is multiple choice. It follows the (so far) standard Coursera structure. Seven weeks of online lectures (around 1.5 to 2 hours per week), with mid-lecture quizzes and a multiple choice assignment each week. There is an extensive reading list (all available free online), but only once can I remember details in the reading being required for a quiz question. The videos consist of a lecturer standing beside a large TV displaying relevant images. The lecturer appears a little uncomfortable in front of the camera, but otherwise production and content quality is high.
With around 10 hours of lectures to cover ancient Greece upto Socrates, the pace of history is quite fast. Thus this course is a little introductory. An impression confirmed by the very easy weekly tests. These multiple choice quizzes give you the answers at the end of each attempt and can be attempted three times without penalty. I can not see how anyone could get less than 100% with a very small amount of effort. After Homer, content is heavily focussed on the Persian Wars, Sparta, Athens and later the Peloponnesian War. Unsurprising as these are the main players and events in the classical period – and also the best documented.
This is a good short introductory course on (mainly classical) Greek history with an especially good set of suggested readings. For a more detailed history of ancient Greece pehaps consider Yale’s CLCV 205: Introduction to Ancient Greek History.