If you created your client's site it's just a case of creating the page and posting it up. If you didn't create the clients site, then perhaps you could create a replica page or a complimentary style page for the blog for your customer and publish it to a blog folder onto your customers host... I hope this makes sense? If you look at my blog you'll see it's in the style of the website [though slightly different] and I just upload this to a blog folder at my host. Then to help promote the blogs, I use FB, pintrest, the best of etc as well as the onsite news page with links to the blogs that are written...

I hope this helps you.