How to manually place 0.5mm pitch bga
There are services that will place components like this for a fee.  I think last time I got a quote from this place, it was like $25 for the service and I had to handle all the shipping and parts and such.  I didn't need it in the end, but I was glad I found the service.

A simple google search returns places such as:


Asian Circuits
Circuit Technology Center
Circle Prime


I haven't used any of these but there are services that will mount the BGA for you.

If you can't wait however long it takes for them to do the mounting, you could try to make some sort of placement stencil, although if you don't have the most steady hands, I doubt that the stencil would assist you in the margins you need.