Genzyme Genetics in Santa Fe has training classes periodically when they need new techs. Amnios, CVS, bone marrow, blood, tissue culture, chromosome analysis...you get to learn everything.
I was hired by them several years ago, went through the program and stayed on with them for 4 years. It's not a bad deal- you get paid to be trained and you get good benefits while living in a nice area, with opportunities for advancement at a fairly rapid pace.
I'd hate to be a director, though- to go through med school/grad school and than get stuck doing paperwork and management.