Depending on the platform, your client might already have access to an m.domain mobile site. Some of the older platforms, like Volusion, haven't even offered responsive designs yet, which is part of what makes them so expensive for their customers. They basically have to pay a company for a complete template redesign.
In my opinion, the responsive design is best practice for SEO, but an m.domain site would improve user experience which can lead to higher CTR and higher conversions. If your client cannot afford to move just yet, then the m.domain is the lesser of two evils. It will improve customer experience and hopefully conversions, and then maybe moving to a responsive design in 6 months would be an option.
I just went down this road with the company I work for. We were in Volusion and just simply out grew it. So we moved to Big Commerce. With the size of our site, it cost us about $1400 a month. The responsive designs were free, and they handled the entire migration for us. At the end of the day, the sacrifice of changing platforms didn't cost us much more than we were spending with Volusion, and the benefits of improved SEO and User Experience will pay for the swap within months. I am not sure what your current situation is, but if you haven't looked into Big Commerce, I would definitely try. It can't hurt to present all three scenarios to the client. At least they will be able to weigh the pros and cons of everything. Staying where they are without an m.domain, staying where they are and adding an m.domain, or moving to a more advanced system like Big Commerce with a fully responsive design.