What’s the best way to negotiate a good booking price?

I don’t know what tactics you’ve been using up this point, but here are my two top pieces of advice.

1. Let the artist’s rep know that you’re serious by giving them a firm deadline to respond and come to an agreement with you. Otherwise, they could wait around for an opportunity to get the upper hand. A deadline puts the pressure on to come to a compromise. This can also help to let you know how interested they are because if they’re working with you to meet the deadline you know it’s an opportunity they don’t want to miss.
2. Don’t look desperate. You need to make it clear that if negotiations don’t go your way you are willing to walk away from the deal. And it should not be a bluff. You have to be able to end negotiations rather than make a deal that’s unfavorable to you. Above all, remember you are making a business decision.