Whether Romeo and Juliet by William Shakespeare should be considered a tragedy or not and whether his plot relies to heavily on the use of coincidence are actually not related questions. One is a question about genre and the other a question about the quality of the plot construction.
A tragedy is a play in which there is an action of a certain seriousness or magnitude, involving characters who have some element of greatness , in which the (usually unhappy) ending is in some way unavoidable. Coincidences, and deus ex machina endings, can be part of tragedy; it also should be noted that there are both good and bad tragedies and ones that are well and badly written.
As for whether the plot is too contrived, it should be noted that realism was not a general attribute of tragedy, not were plays in the Elizabethan period expected to mimic every day life in the way of most contemporary popular dramas.