"Now the city has to find a way to appease them, without looking mean & uncharitable."
While I totally agree that the city SHOULD help in finding a more suitable place for this to go on, it is not the cities responsibility to do so.
You misunderstood: it's the city officials that wrote the relevant law against feeding people, and it's the local businesspeople who are demanding that it be enforced. The city needs to placate the businesspeople, [they need their support] without appearing 'heartless' to their constituents [who didn't complain, because it doesn't bother them].
It would be good if the city helped solve the problem, as they wrote the law that caused it, but the sudden push to enforce the law is almost surely coming from local businesses. Which makes them more responsible for finding an amicable solution, IMO.
I agree, it would be FAR better if local business found a way to sponsor this and help to locate a better site.