9 months old is smack bam in the middle of arsehole. I know because my springer is 10 months.
I think, for me, it comes down to how the older dog is handling tellings off. Some dogs handle it really well and while it might be noisy and they might snap, you can see that there is no real force behind the snap/bite and snarling is done when the pup is doing something rude (going near face, genitals, hip bumping, putting paws on top of older dog etc). The older dog may even rush at and pin the younger dog, but again without any real force. In these cases the older dog is likely to remain fairly calm and in good spirits, except when actively telling off.
This I would allow to happen, only interfering if the younger dog was not giving in and appeasing the older dog or if the older dog was starting to get upset or stressed. Then I would use an interrupt signal ("uh-oh") and remove the puppy. I would also interrupt if the older dog does not discipline appropriately or if there is a large power in balance between the two dogs.
As an example, my springer lives with 2 older JRTs. One (the bitch) is always giving him a ticking off but always does it when it is fair, always her 'bites' are controlled (I know because my hand was once accidentally in there and she had no force behind it) and never seems upset by it. In short, despite being much smaller she is perfectly capable of taking care of the scenario and appears to be a very fair teacher. I've noticed that springer has just started to show signs he is listening and stops whatever he is doing when she says so.
The other JRT is a little male who has no teeth and no social skills. He doesn't know what is appropriate and so any growls from him come from a place of fear and so sometimes unfair (i.e. he may growl even when the springer is not doing anything). With no teeth and little strength he is also massively disadvantaged. Springer is never allowed to upset him and I always intervene.
I would leave springer and bitch alone together. I would not leave springer and dog alone - probably ever.
However, in all cases food, chews, toys are never left lying about. You can't just give them one each and hope they understand - I think the guidelines are that if you insist on doing this you need at least 2 x the items per dog (2 dogs = 4 identical toys). It's easier not to and just pick everything up.
Walking them together is great. If he cannot behave off lead then walk him on lead.
Praise and treat the puppy every time he leaves the older dog alone - you are looking for very simple gestures like him walking past her and not bothering her. Anytime you spot this, praise him. Anytime you spot puppy lying down and not bothering older dog, treat.
Try and find spaces the older dog can be undisturbed. For ours, they each have an arm chair and when they are on the chair the puppy is not allowed up. They know they can relax there because we will run defence, if needed. In the early days that meant I literally sat on the floor in front of the chair and rejected the puppy each time he tried to get up. These days he rarely bothers trying. They also have spots on different rooms - e.g. under my desk is a 'safe zone' for the bitch and she often comes and sits under there while I am working.
I also agree you may be over walking the cocker. If he's not getting around 14=16 hours of sleep a day, he is probably over tired. An over tired puppy is even more of an arsehole than a well rested one.
I have no idea if your dogs will ever get along together (I am guessing they will) but I would not be giving up hope until puppy was properly mature (at least 18 months old).