That's what we really mean when we say “have a good one.”
Wishing somebody happiness rather than goodness is more specific. “Good” is a loose term; it assumes that things generally go bad instead. “Have a good one” is a therefore a warning of impending doom while “Have a happy one” is uplifting. It implies a smile and pushes a positive attitude.
Words have huge emotional power. What you say to other people dictates their feelings. The same goes for the things you say to yourself. We typically act upon how we think.
Next time you're saying goodbyes try wishing someone “a happy one” rather than “a good one.” You may get a smile of confirmation in return. You'll feel better about yourself too.