Vehicular ad hoc networks (VANETs) have a potential to promote vehicular telematics and infotainment applications, where a key and challenging issue is the design of robust and efficient vehicular content transmissions to combat the lossy inter-vehicle links. In this paper, we focus on the robust optimization of content transmissions over cooperative VANETs. We first derive a stochastic model for estimation of time-varying inter-vehicle distance, which is dependent of the vehicle real-time kinematics and the distribution of the initial space headway. With this model, we analytically formulate the transient inter-vehicle connectivity assuming Nakagami fading channels for the physical (PHY) layer. We also model the contention nature of the medium access control (MAC) layer, on which we are based to evaluate the throughput achieved by each vehicle equipped with dedicated short-range communication (DSRC). Combining these models, we derive a closed-formed expression for the upper bound of the probability of failure in intact-content transmissions. Based upon this theoretical bound, we develop a robust optimization model for assigning content data traffic among different cooperative transmission paths, where the objective is to minimize the maximum likelihood of unsuccessful content transmissions over the cooperative VANET. We mathematically transform the optimization model to another equivalent form, such that it can be practically deployed. Finally, we validate our theoretical development with extensive simulations. Numerical results are also provided to confirm the power of cooperation in boosting the VANET performance as well as demonstrate the advantage of the proposed robust optimization in terms of content data reception reliability.