A path without long meditations? I meditate for the purpose described by the Dalai Lama (in his book The Heart of Meditation: Discovering Innermost Awareness):


  To achieve a friendly attitude, a warm heart, respect for the rights
  of others, and concern for their welfare, we must train the mind. The
  essential objective of mental training is to cultivate an attitude of
  compassion and calm


After 30-60 minutes I am calm and aware, but seeing no further benefit in sitting longer. I don't buy the idea that the Buddha's teachings were only available to the select few who can achieve special meditative states. 

Are there any teachers or traditions that teach a path that does not rely on long meditations that last for hours?

(The closest I know of is the Insight Meditation Society, and while they don't appear to emphasize jhanas, they do hold meditation retreats.)
The Buddha's teachings were often tailored to the audience he was addressing.  Teachings like karma, merit making, and securing a good rebirth are available to anyone regardless of how much time they wish to dedicate to meditation.  If you are after true liberation, however, there are no shortcuts.

There is a koan that goes something like this:


  Nangaku (Ch. Nanyue) asks, “What are you doing these days?” 
  Baso (Ch. Mazu) says, “These days Dōitsu just sits.” 
  Nangaku says, “What is the aim of sitting in zazen?”  
  Baso says, “The aim of sitting in zazen is to become buddha.”  
  Nangaku promptly fetches a tile and polishes it on a rock near Baso’s hut.  
  Baso, on seeing this, asks, “What is the master doing?” 
  Nangaku says, “Polishing a tile.” 
  Baso says, “What is the use of polishing a tile?”  
  Nangaku says, “I am polishing it into a mirror.” 
  Baso says, “How can polishing a tile make it into a mirror?” 
  Nangaku says, “How can sitting in zazen make you into a buddha?” 


You can actually achieve enlightenment without ever sitting.  Since this is going to be my last post on this site, I'll candidly tell you that my first truly deep kensho experience happened before I ever met my Zen teacher.  In fact, it happened on my way to Wendy's to buy a hamburger!  Things like this do happen from time to time.  Unfortunately, this has led a lot of people in the modern age to read this koan as saying that consistent, long periods of meditation are not required for liberation.  That's rubbish.  More poignantly, one of the things this koan is saying is that there is no transactional relationship between enlightenment and zazen.  1,000 hours of meditation does not equal 1,000 credits of enlightenment.  Instead, meditation creates the conditions for enlightenment to occur.  Think of it like planting a garden.  Seeds grow all on their own in the right conditions, but as anyone who has planted a garden will tell you, getting that garden started is a lot of work.  You have to establish decent soil, you have to make sure that your plot has a good solar aspect, you have to ensure that there is adequate water, and you have to sow your seed.  Some gardens need more remediation to get going, others less.  And even then, once your plants are started, your work still isn't done.  In some ways, it's just started!  Now, you have to maintain the plot.  You have to weed it, ensure that it has the right amendments, and you have to keep the critters out.  

Buddhist practice is no different.  The seed of enlightenment will grow in a plot tilled with moral discipline and meditation.  For some people, this may happen quickly.  Their karmic soil is fertile and will allow wisdom to grow with little effort.  Others can sit wholeheartedly for decades without experiencing daikensho.  But in either case, the better conditions they create, the better chances they have of seeing success.  Moreover, once they have had an enlightenment experience, the easier it will be for them to maintain it.  As is often the case with spontaneous kensho, as deep as my first experience was, it only lasted for a couple of months.  Eventually, it began to fade - overwhelmed by karmic weeds that could reestablish themselves since I wasn't maintaining my mind with an equally deep meditation practice.       

You never reach the end of the path.  There are always deeper strata of karma to tend to - even after enlightenment.  You need sharp tools and strong back to reach the really subterranean stuff.  You develop both with sincere, dedicated, daily practice.  I'm not going to lie, sometimes that work can have the character of drudgery.  Your legs will hurt, you will get frustrated, and you will even be bored.  Let me assure you, however, that as your practice grows, this very same practice will become absolutely transcendent.  In time, meditation will become your favorite thing in the world.  It truly is a wish bestowing gem.  And it is one that is available to everyone.