There is only one thing left - contacting a recruiter directly.
You can find any employer contact information on the Internet very easily using websites like LinkedIn. You can find HR managers that have posted job positions, and if you dig deeper, you can find the names of managers and supervisors you would work for.
When you have finished a targeted resume with a cover letter, write an email to a recruiter that you are interested in the company and that you want to apply for the job position. Here's an example of how an email could look like:
Mr. John Black,
The purpose of this letter is to explore employment opportunities with XYZ and apply for the Project Manager position. The enclosed resume will furnish you with details concerning my experience and capabilities.
Thank you for your time to get to know me.