On July 4th, I went fishing on the Blackfoot River. The water was very low...about 18-20 inches below normal for this time of year. The lower section of the river above the reservoir was also full of carp. I caught one 20" hybrid on a Stimulator and a 36" carp (~15 lb) on a stonefly nymph.
I have never sight casted to a carp before and it was interesting to toss out the fly in front of its nose and watch it gulp it down. After about a 20 minute fight on my 5 weight fly rod, I was able to land the carp. I tried to catch a few more carp but went without success. Trying to get my fly down deep enough to the carp in the faster water was difficult.
Based on this experience your best bet for the Blackfoot River this year would be a bow and bowfishing kit to shoot the carp. Or to try to catch them on your fly rod. All of the best holes on the upper Blackfoot River were full of carp. Usually the Idaho Fish and Game has a carp trap in the river but it appears that this year they have either removed it or the carp found another way around. Regretfully the carp push out the trout and make trout fishing mediocre at best.