May, June, September, and October are the best months for private tours in Croatia. It is late spring and early autumn in those periods in the Mediterranean.
It is perfect because the beaches and the streets are not that crowded like in July or August.
The weather is still pleasant and sunny, so you can still swim or sunbathe without the big crowds and higher summer prices. April and November are usually too cold to go to the beaches, but the weather is still perfect for hiking, biking, or sightseeing.