The Celestial Manipulator will allow you to set the time of day as well as setting weather such as rain or thunderstorms. This process requires a lot of power but gives you the freedom to even stop time and have it be daytime all the time.
Right-clicking the Celestial Manipulator will bring up the weather options; from this menu, you can stop the rain, summon a storm or start and stop the rain. The bottom bar will display the amount of power the Celestial Manipulator has stored; as you use it to control the weather and time of day, this bar will drain if not connected to power.
On the top, you can select the time tab. This tab will have options for you to stop time and set time. This process also requires power and has a little animation when the time of day is changed.
This machine can also be manipulated with Redstone, which you can activate or stop via Redstone; combining this with the rain sensor or daylight detector could allow you to have constant days with no rain.