Would you like to save the delineated image or the boundary alone or a binarized image ? Process is not the same.
However i suggest to use the ImageJ software for contouring and i think there should be some DICOM plugin for saving the result. If not maybe matlab would do the job.
As suggested, you could use ImageJ or Matlab code. Or you could simply outline the region in MRIcro and save it as dicom format or save it as a nii (or Analyze volume) and then convert it to dicom format using XMedCon or SPIN. Other options would include using Linux e.g. in FSLview (or FSLeyes), or mrview (part of MRtrix3) delineate (trace) the region, save it as a mask, then convert that mask to dicom format using something like XMedCon or SPIN.
If you use mac, then I suggest you use Osirix (outline the region and save it in dicom format).
The delineated boundary of any object either it is a binary image or the region with gray scale intensities can be saved in either DICOM format itself or Non-DICOM image format. If you want to store it as non-DICOM format then the information is known only to you and your program (while reading and writing). If you want others to understand what information you have stored, then you will have to store it in standard DICOM format. It is generally advised to store not only the delineated boundary, but also the geometrical properties of the shape like centroid, bounding box, area covered in mm2, width of the shape etc.
w.r.t your question, I prefer to store it as separate DICOM file with only contour information (refer to any structure set DICOM file in the internet). Please refer to other replies from the application/tool perspective to store it using different software.