I am assuming that you are looking for breathing exercises. Activities like kototama or chanting could also be considered as breath exercises, but are not mentioned here because they are not directly concerned with the breath.
As far as I have been able to determine, the only aikido style that has breathing exercises is the Ki Society. Koichi Tohei founder of the Ki Society, writes about ki breathing in Ki in Daily Life
. Ki Society member William Reed also writes about ki breathing in Ki : A Road that Anyone can Walk
and Ki : A Practical Guide for Westerners
. Ki breathing is also a topic in Ki-Aikido on Maui
by Curtis Sensei. On line resources include the archives at Hawai Ki Aikido
and Unofficial Ki Society Web Site
Koichi Tohei utilized the theories of Tempu Nakamura and applied them to Ki-Aikido. H.E. Davey, a member of Tempukai, the organization that Nakamura Sensei started, writes about Kumbhaka Breathing in his book Japanese Yoga
Others who have written about breathing are Saotome Sensei in his book Aikido and the Harmony of Nature
and Stevens Sensei in his book about Shirata Sensei Aikido : The Way of Harmony
. Shirata Sensei gives breathing exercises in the section on Kokyu-ho: Breath-Meditation.
The Buddha's teaching on breath can be found in the Anapanasati Sutra
that is given in Larry Rosenberg's Breath by Breath
. This Sutra is also commented on by Thich Nhat Hanh Breathe! You are Alive
A Hindu work that some martial artists have found helpful is Science of Breath
by Yogi Ramacharaka. Originally written in 1904, it is still in print.
Some martial artists learn breathing though the Tai Chi/Qigong tradition. This material is too extensive to be listed here.