There are two parts to your question: finding and convincing.
Finding influencers within your industry verticals should not be difficult as there are numerous influencer search engines as one method.
To start, try:
The second method is manual research. That is a whole topic on its own.
The more important part is the convincing. You can find and reach out to as many people as you'd like but if no one engages with you and takes you up on the offer, then it's a waste of time.
The important thing to understand is that this is no different than any other marketing or sales situation. Influencers are simply people with influence. If you were trying to get them to do anything their motivations will likely be the same as any other human being: value (monetary or otherwise) or status.
Figure out what is important to them and you're halfway there. Understand how they typically engage with brands. Do your homework and be prepared to ask them about the value they can bring to you.
Let me know if you'd like to discuss this further on Clarity.