Dynamic contrast-enhanced computed tomography (DCE-CT) is a valuable imaging modality to assess tissues properties, particularly in tumours, by estimating pharmacokinetic parameters from the evolution of pixels intensities in 3D+t acquisitions. However, this requires a registration of the whole sequence of volumes, which is challenging especially when the patient breathes freely. In this paper, we propose a generic, fast and automatic method to address this problem. As standard iconic registration methods are not robust to contrast intake, we rather rely on the segmentation of the organ of interest. This segmentation is performed jointly with the registration of the sequence within a novel co-segmentation framework. Our approach is based on implicit template deformation, that we extend to a co-segmentation algorithm which provides as outputs both a segmentation of the organ of interest in every image and stabilising transformations for the whole sequence. The proposed method is validated on 15 datasets acquired from patients with renal lesions and shows improvement in terms of registration and estimation of pharmacokinetic parameters over the state-of-the-art method.