I went to Kyoto last Summer and had a decent bit of luck at about the same time of year, I did a trip report here you could have a look at:
http://www.birdforum.net/showthread.php?t=262079
I was a little earlier than this, but we only had one bit of rain the whole week on the last day, and to be honest it was REALLY welcome - we'd arrived in the middle of a heatwave so were suffering through 36 degree heat and 100% humidity or something like that.
Best sites were the Imperial Palace Gardens - it contained most of the lifers I got that week, including the brown hawk owl, there is a sign (in Japanese) where they are with little cartoon owls on it, but for approximate directions look at this map:
http://photoguide.jp/pix/albums/kyoto/kyoto-shi/gosho/kg235-20091104_0520.jpg and it's in the block directly above the solid light green block with all the brown spots. It's a short distance west of a water fountain that bird photographers use for to get the smaller species - I had Japanese Tit, Varied Tit and Japanese White-eye among others there. Black Kite, Oriental Greenfinch, Large Billed Crow and Brown-eared Bulbul were also around. However,
BIG WARNING - get insect repellent - something there (not entirely sure what) bit us a lot, mainly in the legs. My girlfriend still has marks visible on her legs a year later for those bites so not something you want to mess around with.
The Rivers should get you a bunch of species too, I didn't do any specific bird-watching beyond a casual stroll down the rivers right in the middle of the city and saw Japanese wagtail, asian house martin, four species of heron, oriental turtle dove, spot-billed duck and black kites easily. Also at least two different species of bats, but I don't know enough about bats to have a clue what they were.
My favourite place in Kyoto was however Arashiyama - it's very much a scenic rural suburb to Kyoto and it has the river running out of the mountains into the city there. The tourist highlights are the Japanese macaques at the top of the hill and the bamboo groves, but didn't see that much in the way of birdlife for either.
What was worth doing however was just walking along the track alongside the river on the monkey side into the forest, and it's just really beautiful there, and if you have listened to the advice of insect repellent and aren't constantly scratching in agony, you'll probably be able to explore further than we did. There isn't much on the water past the town, but forest birds will be all around you and it's seriously one of my favourite places I've ever been.
On a more general tourist note - the Shogun's Palace (Nijojo/Nijo Castle) is well worth a look, inside they have loads of beautiful painted panels and you get to walk across a nightingale floor (kind of like walking on a giant wooden xylophone) is possibly an easier experience than getting into the Imperial Palace itself (which requires prebooking) and is well worth a look. Nishiki market is also a great place to try out street food.
Also, I can't remember what it's called, but if you come out the Eastern end of Nishiki you enter into a big undercover shopping street. If you walk north a bit you should come across a shop on your left with loads of old books in the window, and if you go inside, they sell loads of beautiful antique prints of all manner of subjects, and if that's your cup of tea, you can get some real bargains - I bought a really nice 19th Century print for my parents as a present for what is probably about $12.
As I see you are heading off tomorrow, send me a private message if you think of anything specific you'd like to ask.
