Managing agent is the phrase boards use, and the category term is not
The words your buyer types are local vocabulary, and a national keyword template does not contain them.
A co-op board does not go looking for a property management company. It looks for a managing agent, because that is what the term is here, and it is the phrase that appears in their minutes, their contract and their conversation with the building next door.
Build the list from that vocabulary out. Managing agent for a small co-op. How to change managing agents. Condo management company Brooklyn. Self-managed building looking for an agent. Those phrases carry less volume than the category term and they carry a buyer.
Start on exact and phrase match. Broad match drifts faster in this trade than almost any other, because the surrounding language is saturated with rentals, jobs and software. Add the broader variants later, once the search terms report has taught you what the auction thinks you mean.
Write ad copy in the same register. An ad that says we manage co-ops and condos from ten units up, financials on the fifteenth of the month, will outperform one promising exceptional service, and it does the qualifying work before the click is paid for.