I do not try to space my clients, other than to take no more than 4 women per month. The most "dangerous" spacing for me seems to be 3 weeks apart, much more so than those due the same day/week!
Even if you were only taking one client every 6-8 weeks, you really do need backup in the event that you are sick, out of town, etc. I would backup a new doula who was not charging, or help her connect with another new doula in the area... Perhaps you can find someone?
It's important for clients to understand what will happen if we are not available for their births. I always discuss this with folks before they sign my contract. If you don't have a backup, I really do think you should make this clear to your clients before they sign on -- "I don't have a backup, so although I am almost always available, if I am sick or at another birth you will not have a doula." To me, it is so hard to imagine someone who had counted on doula support and then didn't have it! So she needs some time to wrap her brain around that possibility.
On a sidenote, I would encourage you to think about charging SOMETHING for your certification births, even if it's just $50 or $100, or a barter. I have never done a totally free birth, and have often seen sister doulas struggle when they do so... It seems that many folks do not take your services so seriously or treat you with as much respect when they have ZERO financial investment. You will have expenses for every birth, it's a shame to LOSE money on this lovely but challenging work.