i've had my oldest kid [yoshi, a cat,
not declawed] for about 11 years. the next oldest is about 6 years [holi, a basset]. we brought holi home when she was 6 weeks old. yoshi did
not like that strange thing wobbling across the floor to things it couldn't really see. yoshi stopped sleeping with me for several weeks to show his disapproval. eventually, yoshi tried to play with holi a bit and holi tried to play with yoshi a bit. but holi would often get too playful so yoshi would ... i spied and witnessed it ... place a paw on each side of holi's face then bite her right on the nose! yoshi never once used a claw. he is my angel boy. we brought in other dogs [temporary & permanent] and he decided they weren't worth his time.
now we have 2 dogs and a foster [who's not experienced with cats or house-bunnies], 2 cats & a kitten [they will never be declawed or outdoor kids], 2 rabbits. the 2 cats have decided that as long as the dogs mind thier Ps & Qs, they will let the dogs stay; they will smack if their personal space is intruded upon. i respect this because they do not go overboard and have their own space to get away from everyone.
the kitten is a bit of a different story. i've been her mama since hubby found her at around 5 weeks old. when we found rosie, dusty got jealous and would smack [with claws] rosie for no reason. since dusty is only 6 months old & rosie is fearful of all things, i have been disciplining dusty. it took a few weeks but i think the problem is resolved now.
in the end, everyone happily lives in the house. actually, most of the squabbles are either between the 2 humans or a pair of cats
.
it sounds like your cat will not run away and that is the main motivator for dogs to go after anything. i would keep the cat inside, be sure he has his own space to retreat to,
be sure to give him at least as much rubs and attention as before the pup arrived, and give it time. i'll bet one day you will suddenly realize that things have been going well.
good luck and i hope to eventually see positive news