Both corporate gigs outside of 121 I got because I no only sent in a "hiring package" (more below), but I also came a knocking on their door within a week of sending my "hiring package."
Look - make it easy to hire you. I was underqualified for both gigs, but both gigs put me in brand new jets (mid size and large cabin). In both circumstances, the CP told me that I was hired not so much because of my experience, but because I made the decision to hire me a no brainer.
Here is what you do. Go to Office Max and buy a 1/2 inch binder (buy 2 or 3 of em), buy some nice heavey resume paper, and some plastic page covers. Go home or to Kinkos and make COLOR copies of all your cirtificates, medical, diploma, FlightSafety type rating certificates (if you have them). Print them out on that nice resume paper you bought and print them in COLOR. I recommend boardered paper with the title of the page on the top (for ex: the page with your pilot cert should be titled ATP Pilot Certificate" or the like). Slide the copies into the plastic sheets and put these sheets in your 1/2 in binder. Then, print out your cover letter and resume on that heavy weight paper, slide into plastic cover sheet, put in binder. Add anything else you see fit - letters of recommendation, diploma, award or two from anything, etc. Don't have more than 8 or so pages - all in plastic cover sheets in your binder. Then, print out a table of contents and place it as the first page in your binder, of course it should also be in a plastic cover sheet. Then, the icing on the cake is to find a picture on the net of THE airplane you're applying for - heck go take a picture it taking off or landing. Using MS Word or something similar, make a page to insert into the binder's cover. Have your name at the top and your phone and e-mail at the bottom. Print this in HIGH COLOR with a border - make it look 110% PRO. Put together 2 or three of these binders, in case you are interviewed by more than one person.
Send one of the binders overnight FedEx to the job you want. Follow up IN PERSON a few days later if you don't hear anything. At this point, you will get the interview. Then, bring your other binders, with updated resumes if you've flown in the meantime, for anyone else who may be interviewing you.
I've used this strategy for 3 jobs I was underqualified for - all 3 gigs were flying brand new glass cockpit jets from mid to large cabin with all payscales. The last time I used this gem, it landed me one of those 1 in 1000 91 gigs in an airplane that still blows my mind today with a schedule that is a total joke (100 hours in the last 6 months) for a salary that is nearly ridiculous in my opinion.
Again, every time they told me I got the interview because of that binder and knocking on their door a few days / week later. The interview is a cakewalk if you know yourself and you are confident, humble, and can show them taht you go the extra mile when needed - they can depend on you and you're not an hour builder.
Let me know how taht works out for ya.