In general, normal lens cleaning fluid sold by a reputable camera store is intended to be safe for coated lenses. Modern lens coatings are fairly durable, and there’s no reason to assume a cheaper product will damage them just because it costs less.

The bigger risk is usually cleaning technique, not the fluid itself. Lens coatings are thin, and aggressive rubbing or scrubbing is more likely to cause wear than properly used lens cleaner. Use only a small amount of fluid with a clean lens tissue or microfiber cloth, and wipe gently.

So: you probably do not need a more expensive cleaner. A standard lens cleaning fluid from a known camera retailer should be fine if used carefully.