morning, early
晨 centers on the early part of the day: morning, dawn, or the early hours. It conveys the idea of the sun rising and the start of daytime.
晨 combines 日 (sun) and 辰, which here likely represents the early morning or the time when the sun appears. The exact historical role of 辰 is uncertain, but the character clearly expresses morning through the sun component.
The sun 日 rises above 辰, like the morning sun climbing over the horizon. Picture the early light spreading as the day begins.
For シン, imagine the morning sun shining on a shiny new day: shiny -> シン, and the early light makes everything gleam.