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Background and Purpose: Treatments on combined Magnetic Resonance (MR) scanners and Linear Accelerators (Linacs) for radiotherapy, called MR-Linacs, often require daily contouring. Currently, deformable image registration (DIR) algorithms propagate contours from reference scans, however large shape and size changes can be troublesome. Artificial neural network (ANN) based contouring may alleviate this issue, however generally requires large datasets for training. Mitigating the problem of scarcity of data, we propose patient specific networks trained on a single dataset for each patient, for contouring onto the following datasets in an adaptive MR-Linacworkflow. Materials and Methods: MR-scans from 17 prostate patients treated on an MR-Linac with contours of Clinical Target Volume (CTV), bladder and rectum were utilized. U-net shaped models were trained based on the image from the first fraction of each patient, and subsequently applied onto the following treatment images. Results were compared with manual contours in terms of the Dice coefficient and Added Path Length (APL). As benchmark, contours propagated through the clinical DIR algorithm were similarly evaluated. Results: In Dice coefficient the ANN output was 0.92 +/- 0.03, 0.93 +/- 0.07 and 0.84 +/- 0.10 while for DIR 0.95 +/- 0.03, 0.93 +/- 0.08, 0.88 +/- 0.06 for CTV, bladder and rectum respectively. Similarly, APL where 3109 +/- 1642, 7250 +/- 4234 and 5041 +/- 2666 for ANN and 1835 +/- 1621, 7236 +/- 4287 and 4170 +/- 2920 voxels for DIR. Conclusions: Patient specific ANN models trained on images from the first fraction of a prostate MR-Linac treatment showed similar accuracy when applied to the subsequent fraction images as a clinically implemented DIR method.