You need to have a really good LinkedIn (LI) Profile: think of getting a LI coach...they are not that expensive. I recommend you consult LinkedIn to find employees who work for that company. Do you know any of them? If so Connect and ask to meet for coffee. If not, send him/her an InMail asking if you could take them out for coffee before work, or something after work. If it turns out the company and your LinkedIn targets are not local, make efforts via LinkedIn to meet with several of them during a few-day visit. All this gets expensive (keep track of expenses for tax purposes) but it works. Network this way to gain rapport with current employees who can then introduce you to (potential) hiring managers. In my experience, even the best written resumes and cover letters are often not productive. View my Profile and contact me if you wish.

Although I have never done it myself but am seriously thinking about it. The girl I used to work with wrote to 4 jobs even though the job ads were gone and got 3 of the jobs. I think it shows initiative and the company may not have advertised a job yet your are peperfect for. Good luck.