Initially when a customer says this I assure them I'm not trying to replace their current web developer, can work on it together with them if that'd be most advantageous, show them some of my previous work, etc.
Thus far, most folks I've done this with have ended up having their current web developer take care of it, leaving me out.
I started replying to such folks with the following:
"No worries; I hope they take great care of you.
One more question, if I may.
I am sure that you have in your network many small business owners similar to yourself. I am sure some of them would benefit from having a mobile site, and do not have a good reliable web designer they already work with that can take care of it for them. I was wondering if you might be willing to send a note similar to the following out to a few (~10-15) such individuals?
"Hey, I just wanted to share this information with you guys. I recently had someone reach out to me regarding setting up a mobile version of my website. After some consideration, I decided to actually let my current web designer do it. However, I know some of you either manage your own site, or don't have a solid reliable web designer that can take care of this for your site, so I thought I'd forward along the contact information for the guy I mentioned. He informed me that (according to google) over 20% of all web traffic is currently mobile, and it'll be over 50% by the end of 2013, so seems like a worthwhile investment. Here is his info:
If you would be willing to do so, I would be most grateful, as I'm sure the folks you send it to will be.
Happy holidays, and all the best to you and yours!"
I have done this a few times, and have had a couple that are willing to do so.
Sharing this right now because I just got a sale out of it.
May the force be with you.