When it comes to finding a job, sometimes you have to take the bull by the horns. Instead of sitting around looking for a position that matches your skills set and experience, write a proposal for a new job description and present it to the company for which you'd like to work. A proposal that explains why the position is needed and why you're the best person for the job shows initiative and critical thinking skills and will likely get the attention---and possibly even admiration---of someone with hiring power.
Research whether other organisations similar to the one where you plan to submit your proposal have someone in the position you hope to create. In particular, look at competitors of the company where you'd like to work. No organisation likes to be outdone, so you'll want to show how creating this position will help the company stay competitive.
Start your proposal like you would any cover letter, by placing your name and contact information at the very top, then following that with the name of the person and company the letter is addressed to, followed by today's date. Address your proposal to the hiring manager or the person who would oversee this position.
State that you are writing to propose a new position, which you would like to be considered for, and name the position or job title you are proposing.
Explain why it's in the company's best interest to create this position. This is where your previous research will come in handy. Note how the position can advance the company's goals, and how similar positions at other organisations are helping them. Use bullet points to draw the eye to important points.
Provide a detailed description of the job, including the key roles and responsibilities and qualifications. Be thorough, so that the person reading the proposal isn't left with unanswered questions about the position.
Explain how your skills set and experiences are a perfect fit for the position. Listing past professional achievements is a good way to showcase your abilities.
Add a detailed cost/benefits analysis. This should explain what the company can expect to gain for what it will spend to pay you if it hires you for this position.
End by reiterating, in a succinct manner, why the company should hire you for this position and whether you expect to hear from the person you addressed the letter to or whether you plan to follow up with a call or e-mail.