How to get sponsors for a small event

Stop selling logo placement
Gold, silver and bronze tiers are borrowed from conferences with thousands of attendees, where a logo is genuinely worth something. At a dinner for twenty, nobody is buying visibility. They are buying access to the specific people in that room.
Sell the room, honestly
Tell a prospective sponsor who actually attends: the roles, the kinds of companies, roughly how many. A sponsor who knows exactly what they are getting and says yes is worth more than one who agreed to a vague number and feels misled afterward.
Give them something a person will see
A logo on a slide that shows for a minute is not a deliverable. A place on the page every guest actually opens, before and after the event, is. Intro Connect builds a sponsor tile from a pasted link, so this costs the host no design time and gives the sponsor something durable.
Ask for less than you think
A first sponsorship that is easy to say yes to buys you a relationship and something to point at next time. Hosts routinely ask for a large number once, get declined, and conclude that sponsors are not interested.