Stereotactic body radiotherapy (SBRT) is a well-established treatment modality for liver metastases in patients unsuitable for surgery. Both CT and MRI are useful during treatment planning for accurate target delineation and to reduce potential organs-at-risk (OAR) toxicity from radiation. MRI-CT deformable image registration (DIR) is required to propagate the contours defined on high-contrast MRI to CT images. An accurate DIR method could lead to more precisely defined treatment volumes and superior OAR sparing on the treatment plan. Therefore, it is beneficial to develop an accurate MRI-CT DIR for liver SBRT. To create a new deep learning model that can estimate the deformation vector field (DVF) for directly registering abdominal MRI-CT images. The proposed method assumed a diffeomorphic deformation. By using topology-preserved deformation features extracted from the probabilistic diffeomorphic registration model, abdominal motion can be accurately obtained and utilized for DVF estimation. The model integrated Swin transformers, which have demonstrated superior performance in motion tracking, into the convolutional neural network (CNN) for deformation feature extraction. The model was optimized using a cross-modality image similarity loss and a surface matching loss. To compute the image loss, a modality-independent neighborhood descriptor (MIND) was used between the deformed MRI and CT images. The surface matching loss was determined by measuring the distance between the warped coordinates of the surfaces of contoured structures on the MRI and CT images. To evaluate the performance of the model, a retrospective study was carried out on a group of 50 liver cases that underwent rigid registration of MRI and CT scans. The deformed MRI image was assessed against the CT image using the target registration error (TRE), Dice similarity coefficient (DSC), and mean surface distance (MSD) between the deformed contours of the MRI image and manual contours of the CT image. When compared to only rigid registration, DIR with the proposed method resulted in an increase of the mean DSC values of the liver and portal vein from 0.850±0.102 and 0.628±0.129 to 0.903±0.044 and 0.763±0.073, a decrease of the mean MSD of the liver from 7.216±4.513mm to 3.232±1.483mm, and a decrease of the TRE from 26.238±2.769mm to 8.492±1.058mm. The proposed DIR method based on a diffeomorphic transformer provides an effective and efficient way to generate an accurate DVF from an MRI-CT image pair of the abdomen. It could be utilized in the current treatment planning workflow for liver SBRT.