Generally speaking, you can group the planets into inner and outer planets.
Inner planets are most likely to be seen around dawn. Some are so closely tied to the sun that they're known as Dawn Heralds. Most or almost all of the inner planets will be available then and are gradually staggered around that time so that throughout the day there will be some planets available. Around dusk they are mostly gone and by late evening there will never be any inner planets in sight. You'll also find a quirk of them being sun chasers in that they'll sometimes be in the sky but not viewable because they're too close to the sun. They'll still work for Invocation of the Spheres in this case, however, just not available for observing or studying until they've distanced themselves from the sun.
Outer planets can be visible at day or night, depending on where the orbits are relative to Elanthia. It is entirely possible to find yourself in a situation where few, if any, planets are available at night. Due to the slow orbits of the extreme outer planets this tends to be a seasonable problem and doesn't crop up every year.
The planets in order from the sun are:
The sortable starchart is a handy tool to quickly group constellations and planets by season or skillset.