I do believe the practice of morality is mainly relative whether or not absolute morality exists (see: moral sense theory). Rather I view moral relativism as the methodology for testing various moral constructs (Jamesian pragmatic morality). Moral relativism is basically what we do when we engage each other (see: social constructivism) and morality is the artifact of these interactions (see: social constructionism).
My own personal form of morality is a form of reliablism (see Michael Bishop), appended to a utilitarian based social constructivism, buttressed with Buddhist philosophical insights (many which denote a type of methodological pluralism) and reinforced by mutual corresponding theories (i.e., other appreciations).
As I said, there is no single theory I subscribe to, but the combination of various moral philosophies, networked together, forming a modular moral model, work just as well if not better than Christian concepts of morality. Finally, it’s worth reiterating that Christianity, as well as other “religions of the book,” are limited by a dogmatic creed confined to one archaic text. Which, as a consequence, forces Christians (and other religious believers) to either become relativists themselves (rejecting the bad bits and cherry-picking only the best), or else strict legalists (fundamentalists who interpret the law to the letter). Personally, I find such religious dogma to be counter-productive, and often times harmful, when it comes to moral considerations and ethical concerns.