I know of no RA/ATS DMin which can be earned 100% at a distance. Trinity's (Newburgh, RA candidacy) DMin can be earned 100% at a distance.
If memory serves correctly Southern Christian University used to offer a DMin through their leadership school that was totally distance. They got away with it because their leadership school (unlike their theology school) is not ATS accredited. ATS does not approve of any degree which does not have a residency component. And really, when it comes to DMin accreditation ATS is what people look for. However, it doesn't appear SCU is offering their distance degree anymore. And that was the only one of which I was aware. Although, as mentioned Trinity is in the RA candidacy stage (but not ATS). The thing about DMin degrees is that they are almost all field-based degrees anyway -- with short-term residency (often dispersed). In the over-all scheme of things it is pretty convenient.