My wife and I are in Sussex but our son is in Liverpool so we pass through the Birmingham area frequently.
I also travelled up to Coventry once a month for about 18 months to teach a Christian Counselling Course.
So I know your area reasonably well.
Even easier go to Association of Christian Counsellors and click on the link to Find a Counsellor from the menu on the right of the page.
Select your area and if you are looking for someone who works alone or as part of an organization (I would check both lists)
NB This is a UK listing so if any members who are not in the UK read this post it is no use to you. Sorry.
There are a number listed in Birmingham. I just double checked and lots more listed as West-Midlands. If you send me a pm with details of where you live I will see if I can find someone through my contacts.
The 'free holiday' doing housesitting is available to any Christian anywhere in the world. I don't want to use this forum to talk about that so just visit the website and read all about it.