Mike,
Morale is a very difficult thing on GC. I even had to go to the user's guide (its in the "encyclopedia") to see if it said much about it. It does, but it says it in a rather oblique manner.
The factors that affect morale are: planet class, planet population, tax rate, completed morale improving social projects, surveyed anomalies that improve morale, government type (I think I remember this one, but I may be mistaken), mining of the yellow galactic resources (called "happy gas" in the resource definition file), and, perhaps, some other things, like an occasional UP issue or a random event. Some colonization events can also affect morale.
Correcting the morale on a planet can be done by altering any of the above factors, although some are rather difficult to accomplish and some are dependent on pure luck. Planet class can be altered (after it is colonized) by building one of the three planet class altering social projects (soil enhancement, habitat improvement, and terraforming). Populations can be moved to other planets in colony ships or transports, in addition to using them to colonize new planets or conquering the stars of opponents. Tax rate is, of course, obvious (or is it? Be very careful of your treasury. If it goes negative, it can bring morale down catastrophically, in which case, changing tax rate won't help at all). The rest are truly obvious once you know about them.
But don't expect to keep your morale at 100% on all of your planets. That is contrary to the game design (as implied in the user's guide), so don't sweat it. Just try to keep the overall morale above 60% (to keep control of the senate) and individual planets from dropping below 40% (they loose population if below 40% and, at one point on this forum, there had been discussion of carrying over from GC/OS2 the idea of planets with morale below 30% rebelling (becoming rebel planets with no ties to any race)).