How to design proper content placement strategies is one of the major areas of interest in cache-enabled cellular networks. In this paper, we study the probabilistic content placement optimization of base station (BS) caching with cooperative transmission in the downlink of cellular networks. With placement probability vector being the design parameter, non-coherent joint transmission (NC-JT) and coherent joint transmission (C-JT) schemes are investigated according to whether channel state information (CSI) is available. Using stochastic geometry, we derive an integral expression for the successful transmission probability (STP) in NC-JT scheme, and present an upper bound and a tight approximation for the STP of the C-JT scheme. Next, we maximize the STP in NC-JT and the approximation of STP in C-JT by optimizing the placement probability vector, respectively. An algorithm is proposed and applied to both optimization problems. By utilizing some properties of the STP, we obtain globally optimal solutions in certain cases. Moreover, locally optimal solutions in general cases are obtained by using the interior point method. Finally, numerical results show the optimized placement strategy achieves significant gains in STP over several comparative baselines both in NC-JT and C-JT. The optimal STP in C-JT outperforms the one in NC-JT, indicating the benefits of knowing CSI in cooperative transmission.