The grailsApplication object is available within services, allowing this:

package example

import com.example.ExampleApiClient;

class ExampleService {

    def grailsApplication

    def relevantMethod() {

        def client = new ExampleApiClient(
            grailsApplication.config.apiCredentials.baseUrl
            grailsApplication.config.apiCredentials.username,
            grailsApplication.config.apiCredentials.password
        )

        return client.action();
    }
}