Soupdragon - Many vicars/ministers would be happy to come and say a prayer/blessing at a ceremony in your garden, I'm not sure whether you could have a 'christening' in your garden though.
I think the only approach would be to phone round some local clergy. If they can't help, they should be able to suggest someone who will ...
I'm not sure what your background is, but I suspect that you are not a member of a church, or you would be approaching your own vicar/minister (?) You should be aware that some clergy get very stroppy about baptising children of non-regular church attenders, so you may need a thick skin.
Dh is a Baptist Minister, and we don't baptise babies ... we do adults. But on Sunday he is doing a 'blessing/dedication' of a baby of non-church folk. They wanted the baby 'done', but got negative and unhelpful responses from local Anglican clergy. He would certainly be happy to say a prayer/blessing in someone's garden. But from an Anglican/Methodist point of view, this would not be a proper christening/Baptism.
Hope this is helpful - sorry I'm going on a bit.
Your best route might be to chat to people locally and find out which local clergy are amenable.
I'll ask dh whether he thinks any Anglican vicar would to a 'proper christening' in a garden, and will get back to you. In our church it would be important to be in the church, in public, because then the whole church family are there supporting you. But I know many Anglican churches do baptisms 'in private' on a Sunday afternoon anyway, so not sure this is relevant.
I'll stop rambling, and ask dh what he thinks.
Is a 'proper christening' important to you anyway?
What do you actually want, and why? Or is that a bit deep?