One may tend to discussed then if these can be experienced as two as separate states of being - meaning, are we really only able to feel happy when we do not suffer? and conversely, when one is suffering is it then not possible to feel or be happy?
From my own experience, happiness isn’t a thing - instead, happiness is the result of the combination of feelings of the things we live and experience. You are not happy - you feel (or not) happy.
For the ones that may agree with this perspective, this means that the pursuit of meaning, purpose and fulfillment in life as a long lasting challenge may not make that much sense... Sustaining this perspective is the body of research that suggests that happiness is a combination of how satisfied you are with your life (for example, finding meaning in your work) and how good you feel on a day-to-day basis.
In summary, do try to remember that under normal conditions, daily life is filled with simple things (and miracles); from the wonderful people that surrounds us to computer games or a peaceful walk in the park. Somehow we tend to take all for granted after a while, putting in front of us the challenge of thinking about a better way to appreciate and savor the good things of life. If that is the case, try this framework at Happify were you can practice, right now, and get a shot of healthy psychological nutrients.