There are a couple of options available.
First of all, you can use it as a normal dependency and use a factory bean to instantiate your object.
@Component
public class MyFactoryBean {
    private Repository repository;
    @Autowired
    public MyFactoryBean(Repository repository) {
        this.repository = repository;
    }
    public Instance getInstance(Parameter parameter) {
        return new Instance(repository, parameter);
    }
}
If your parameter does not change at runtime, you can provide a bean in your configuration:
@Configuration
public class MyConfiguration {
    private Repository repository;
    @Autowired
    public MyConfiguration(Repository repository) {
        this.repository = repository;
    }
    @Bean 
    public Instance instance(){
        Parameter parameter = ... // value in a config file or static value 
        return new Instance(repository, parameter);
    }
}
Also, you can use the AutowireCapableBeanFactory to inject dependencies as normal for objects not managed by Spring. Remember that you need to use setter injection tough.
private AutowireCapableBeanFactory beanFactory;
@Autowired
public MyFactoryBean(AutowireCapableBeanFactory beanFactory) {
    this.beanFactory = beanFactory;
}
public void doStuff() {
    MyService service = new MyService();
    beanFactory.autowireBean(service); // dependencies will be autowired
}