Where you do the course doesn't really matter when it comes to applying for work as an FI.
One or two schools who run FIC courses will only employ people who did their course. This is mainly for standardisation of training within the company. That way they don't encounter problems with each instructor having different methods and confusing students.
It's about the right time of year to do the course as GA picks up around April May time when the weather is meant to be better, so a few clubs and schools may be glad of some extra part time help or casual cover.
I would probably suggest looking around at some other schools that teach FIC to get a broader picture of who offers what, I have no knowledge of Coulson so I can't comment on them. I'm other side of the country!
Best of luck with it!
HOP