They have the same meaning but comfortable means something soft and relaxing and convenient means something suitable and practical. for instance: He's trying to find a convenient time for your lesson.,It's easy to feel secure when you have a comfortable salary Pleease look at these links: comfort - Definitions available for comfort from Cambridge Dictionary Online: Free English Dictionary and Thesaurus convenience - Definitions available for convenience from Cambridge Dictionary Online: Free English Dictionary and Thesaur

convenient = simple, easy, no problem - It is convenient for me to visit tomorrow morning. - The store is conveniently located nearby. comfortable = happy, content, satisfied - First class is more comfortable than tourist class. - They are very comfortable in their new home. - A bed is more comfortable than a sofa.