Hi Justin
This is a great question. This is going to take a little bit of leg work on your end. Here are the steps I would take:
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Create the blog on your site
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Do some research
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What information is missing in your industry?
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What are users actively searching for?
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Where are they currently participating in conversation?
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What language do they use in search and those discussions?
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How do they digest their content?
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Here's a quick resource on content gap analysis from Edge Multimedia
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Take advantage of great tools like Open Site Explorer and SEMRush to get a handle on your competition and what's working / not working for them
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Build out content on the site based on your research
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Mind your obvious onsite SEO fundamentals (titles / meta descriptions / schema / content length and language / etc.)
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Lay your site architecture out in an easy to use / understand fashion
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Repurpose content through video / images / guides / e-books / how-tos / etc
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Take advantage of internal site search functionality
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What are users searching for on your site?
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Distribute that content through social platforms / industry blogs / email marketing
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Participate in the discussions that are happening in your industry
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Social
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You could take advantage of features like Twitter's Advanced Search and start fielding questions
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News sites
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Industry forums
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Q&As
What I am getting at here is to start building a foundation and engaging your audience. Really start diving in on getting your name and website out there. Start building content that is information based about your industry that users will actually have a use for and keep coming back for more.
From there, you can entice writers by showcasing stats about your site, your community presence, what it is that differentiates YOU from your competitors (you did the research, you have great content in different types, you provide people with answers and they value you for it), and why becoming a contributor to their site will ultimately heighten their own presence.
I would also look into some contributor opportunities for yourself to get your name out there as well as your site. If you start engaging people in different areas by contributing, they are going to be interested in who you are and what you have to offer. Also, start engaging the contributors you are interested in (in a natural, friendly way of course - do NOT ask them for anything in your first interaction). What do they write about? Do they have the same passions you do? Comment on their articles, shoot them an email to say hi, etc...Don't be shy!
Hopefully this helps. Again, this is going to take some time, but take the steps listed above and you will find yourself in a position to approach those writers about joining in on contributing to your website. Good luck!