The concept of copulas is useful to model multivariate distributions. Given a parametric family of copulas, the inference of the parameter vector commonly relies on likelihood-based methods. However, for some copula families, the likelihood may not exist, or may lead to slow or complex numerical optimization procedures. Therefore, it is desirable to consider alternative estimation strategies. A natural approach is to build the inference on bivariate dependence coefficients, where the weighted sum of the squared residuals between the dependence coefficients under the model and their empirical counterparts is minimized. This method has already been used in some applications but in a rather heuristic way. The asymptotic properties of the resulting estimator have not been investigated yet. In this paper, we derive the consistency and asymptotic normality of the weighted least square estimator based on three standard dependence coefficients. Finally we illustrate how our results can be used to address three statistical questions.