The reason co-ops are coming up in your search instead of condos is because you indicated prices between $300,000. - 500,000. Condos are more expensive and start at $500,000. The average condo in New York City is about $1 million. Obviously you cannot afford a condo. If your price point is between $300 - 500,000. all you can afford is a co-op.
You need to face reality that you cannot afford a condo. Co-op buildings are just as nice and you can still build equity and sell it on the open market. The difference is with a co-op you own shares of a limited housing corporation that gives you ownership in a specific apartment. In a condo, you receive a title or deed like a single family house. This is why condos are more expensive than co-ops.
On real estate websites (like Trulia and Zillow) if you were to set your price point from $800,000. - $1 million, your search results would show condos - not co-ops.