4 year old cat doesn't like new kitten

I'm sure this has been posted a bunch in the past, but I'm new to this site and am looking for some advice. I got a new kitten (about 9 months old) last month and my resident cat (4 years old, been an only cat almost his entire life) is really struggling. I keep the kitten separated in her own bedroom most of the day and at night, only letting her out when my resident cat is secured in another bedroom. They are both spayed/neutered, and both act totally fine when they are separate. They are used to each other's sounds and scents and don't have a problem when they aren't in the same room. However whenever I try to give them exposure to each other my older cat starts hissing and growling which causes her to do the same. I have brought her out in her carrier and he just growls, hisses and bats/jumps at it. I don't trust him yet to let them out together freely and it has been almost 4 weeks. Any tips or things I should do differently?

Hi, and welcome to TCS

I think you've hit the nail on the head - your resident cat is really struggling with the addition of your kitten. You need to carry out gradual, phased introductions, always moving at the pace of the least confident/comfortable cat (in this case, your resident cat). Four weeks really isn't long at all in introduction terms - months is usual, and I have known of cases where the process has taken a year or more (don't panic - these are the exception rather than the rule, but are sometimes necessary ).

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I would suggest a Feliway diffuser, or even spray, in the meeting room of theirs.

Be sure they both ar  comfortable with the meeting room, and there are places they can flee to if necessay.  Like some shelves they can jump up into....

Im sure each one is indivdually good friend with you, see you as their Momma.  Try to talk them down, ie talk friendly and convincigly to them, to  smoothe out the tensions...

Try to get them into play, perhaps use a Da Bird toy or perhaps better TWO such, and provoke them into playing simultaneously - but with time both with the same toy.

Thanks! I will be check out all of these articles. 

I've got Feliway diffusers going already, but it's hard to tell if it's working.

And yes, they are both friendly and loving with me, just not each other!