円 and 月 are both graphical corruptions. The original form of the character did not have those components.
靑/青 was originally comprised of 屮 (sprouting plant) and 井, which gave the sound. The bronze script form looked like
In ancient scripts, 井 as a component was frequently interchanged with 丹. The graphical form of 丹 originated as 井 plus a small horizontal stroke in the middle. See, for example, the oracle bone forms
In 靑/青, this happened as well:
On the bottom part, the form which came from 井 morphed to 月, while the form which came from 丹 morphed to 円.
Note that the top has actually been written with several similar components; you may find 青 variously written with 屮/生/木 on the top in ancient times. For clarification, the bronze script forms shown here actually contains 生, but 生 ultimately comes from 屮 with the addition of two horizontal strokes.