I've just been reading an entry on a cousins Facebook page where they have just got the most beautiful new puppy, who is just perfect, however the resident cat has just taken to sitting in her litter tray!!
She is used to dogs so it is only the fact that the puppy is new and probably somewhat more active than she has been used to for many years. She has probably taken to her tray as this is where her smell is and she feels safe but as cats are so fastidious she obviously won't want to be there.
So I wondered what could be done!!
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A bouncing puppy full of energy is probably frightening to an older slower cat so to open up physical escape routes where she can watch but not get approached
may help. Bring some height into her world where the puppy cannot reach, easy access to shelves, tops of units, backs of settees, across mantlepieces, and up cat trees. Here she has gained a whole new level of a world where he cannot get her but she can watch him. It might affect the aesthetics of the room but it can be done.

Place the litter tray where she can use it without fear of an approach, she is feeling insecure. Also add one more litter tray and if it can be given some height or turn it, if it is hooded, so access is restricted for the puppy.
Use a feather rod toy to get her to play AROUND the new puppy but not necessarily with ( Da bird or Frenzy rods, great flying action and most likely to get a response than the short ones in the shops
http://www.da-bird.co.uk).
It will pull her out of the litter tray, she will see him as nothing to be scared of. Play with him at the same time but with something else, a game where he is not prancing around, maybe a training session of sit and down etc.
Potions and Pills
Zylkene can be bought from the vets or online as it is non-prescription. Online is far far cheaper. Its use is to calm and destress animals such as dogs, cats and horses. Most people I have known use it when moving, when fireworks are going to be about and when introducing new cats, dogs or babies to a household. Unless your cat is an angel at taking pills I have found the best way to use it is in food or treats, I use Webbox lick e lix tubes, a yoghurt like liquid which I break the capsule into. Expect it to take a couple of weeks to work and does not work on all animals. However our household now does include five cats and so far so good!!! because of the cost I am sneaky I buy the ones for dogs and divide the capsule contents up as it is the same product for all animals just in different quantities and the capsules are not time release. This should just calm her.

Also Feliway ( http://www.feliway.com/uk/ )can be used or Pet Remedy diffusers ( http://www.petremedy.co.uk ). Feliway comes as a spray to be used in travel boxes or where a plugin cannot be used or a plug in diffuser. The evidence for success is anecdotal, some people swear of its success others say it hasn't done a thing!! Whereas Feliway is a pheromone Pet Remedy is herbal i.e. it includes Valerian etc, it smells like old socks a bit but I have to say if I spray this around their beds they do seem to use them, this also comes as a diffuser as well.
Time to use the vets!
Cystitis is horrible and cats are prone to getting it when stressed, just keep a check on the litter tray for blood or even straining by her. Cats are very, very good at hiding pain. She maybe in there NOT to hide but has the need to go. If she has got cystitis the vets may recommend Cystaid
( http://www.vetuk.co.uk/pet-cystitis-cat-cystitis-c-5_7_1280/cystaid-plus-cystitis-glucosamine-capsules-for-cats-240-pack-p-41 )
be added to her diet and a specific expensive dry cat food. I personally would add a water fountain to encourage fluid drinking, withdraw normal dry food and only feed wet tinned or RAW. Even add more water to the tinned if you can. If she is a kibble only cat try buying "Fortiflora" this is a powder which you can dust over the
tinned food to encourage eating and tastes similar to the stuff they blast the kibble with.
I know this is focussed on only the cat, when such a lovely puppy has entered the house, however she is confused and stressed.
I hope this helps a little, just a few ideas.