I don't think there is a role. I think you need to determine the responsibilities and motivations a person might have for sponsoring and speak to their needs related to it. In my experience, the people with these interests in a company don't reside in just one role.
If they do have a person, then it would likely be someone tied to CSR (Corporate Social Responsibility). The best way to find this person is to see if the company currently sponsors other organizations and contact those people to find out who the key contact is.
I always look for the artifact that the organization is interested in doing something, then follow the trail backwards till you find the lead individual.
Generally sponsorships happen because a person(s) have a personal relationship with someone or they identify that the group will have a good impact on their business in exchange for their sponsorship.
Sponsorships can be done in many different ways...so get creative and you will be surprised how many companies will want to get involved. I have done this many times with non-profits or even for profits and we created a platform to get their brand out and had to start turning away sponsorships.
I work in Sports Management so I would contend that if there is a specific role or department in an organization to contact it would be their Community Outreach Dept. If the company website does mention their presence in the community that would be the direction to. I would also look at the PR dept in the company. Finally I would also do my homework on the company leadership, whether its a board, consortium, a CEO or President. Research their philanthropy if they have done any at all and if not this may be your opening. I would also brush up on the companies current presence in the community as angle to possible get them involved in the community.