Is it necessary for a Buddhist to believe that existence is suffering? It appears that Buddhism depends on a central premise -- that all worldly existence = suffering / dukkha. 

Are there Buddhist teachers or traditions that teach a joyous approach to worldly life?

Are there any teachings that profess existence is a joyous, if sometimes painful experience, or at least a tolerably pleasant experience? An eternal roller-coaster ride of birth-and-death, joy and sorrow, that one need not seek to escape?
The gateway premise is not that "existence is suffering", it is that "something is wrong here". In other words, if you are perfectly satisfied with everything (are you?), if you are clear about the purpose of life, if you are a master in dealing with all possible kinds of situations -- then there is no reason for you to look out for anything at all, be it wisdom or liberation. If that is the case, then you are in a temporary heavenly state (to use Buddhist metaphorical language, wink-wink), which temporarily precludes any motivation to set on a spiritual quest to get to the bottom of things.

However, if you feel that you are not living the life you should be living, if you clearly see society as fundamentally messed-up, and are not willing to be complacent about that, if you are haunted by the underlying feeling of wrongness, of incompleteness, if you feel that something is missing - then obviously you will be very motivated to seek a solution!

Even if life is relatively good - still, if you are any attentive and smart, you may find yourself not being satisfied with superficial success, with solving problems at superficial level -- instead you may want to take a step back and solve the underlying problem, and the problem underlying the underlying problem, and the problem underlying that problem, and so on - you want to get leverage over things, you want to find the fundamental solution, the universal principle... You have a sense that the way you deal with things, however well, still leaves something to be desired - but what?

This feeling of deep buried wrongness, of aching incompleteness, of fundamental restlessness, of subtle unsatisfactoriness - that's what we're talking about here. This is where Buddhism begins: "something is wrong here". This is known as "the ground". You begin with what you have right here and now, the feeling of underlying incompleteness - and you are determined to not stop until you solve this most fundamental of all problems. The having solved the problem is known as "the fruition". And the steps from here to there are called "the path". These are the basic rules of the game. Makes sense, huh? :)