Which are the various causal tests in statistics which can be done in R? I have data for some months, with 2 variables. But I am not able to prove causation in between.
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No statistical test proves causation.
Such relations can be strongly supported from data produced by a particular experimental design. Usually this design associates to a randomised experiment but there is a huge body of work for observational studies as well. (see for example the book on "Explanation in Causal Inference" by VanderWeele or "Counterfactuals and Causal Inference" by Morgan and Wimnship) In any case, the data and evidence we gather strongly imply rather then prove causation. You specifically mention temporal data: in the case of temporal data it might be a lucrative idea to assume a causal relation but this can be a red herring; this matter was extensively discussed on the CV thread on: "Correlation does not imply causation; but what about when one of the variables is time?".
R allows you to try a variety of cutting-edge algorithms to assess causality relations. Off the top of my head I can think of the packages pcalg, InvariantCausalPrediction, CausalImpact to mention three packages one could try. Again, the results from the packages do not prove but provide strong evidence for causal relations.
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