Black Raspberries are not blackberries they are simply Black Raspberries and are no more drought tolerant than red raspberries.
Blackberry canes tend to be larger and more overbearing when mature.
When raspberries are picked, the berry slips off the rasp, leaving it behind. In blackberries, the rasp breaks off where it is connected to the stem and stays within the berry.
If you live in a drought plagued area and are purchasing some berry bushes be certain it is Blackberry not raspberry or even black raspberry.
Once established, blackberries are relatively drought-tolerant, but water stress will negatively affect yield. Mature plants require more frequent, heavier irrigation's than do young plants. For mature plants, most recommendations call for about 1 inch of water per week. (Lipe and Martin, Culture and Management of Blackberries in the US 1984).
Seaberries are hardy in zones 3 - 7. The berries resemble citrus in taste and composition. The berries are the size of a large blueberry and have a citrus flavor, in fact Europeans use seaberry juice as a substitute for Orange Juice.
Tips and Techniques
1. Prepare your beds by adding large amounts of organic material and compost several inches deep. Work it into the soil well, it will help supply much needed nutrients to the plants as well as enhance the moisture retention quality of the soil.
2. Add another 3 to 4 inches of organic mulch around the base of plants to help with moisture retention.
3. It is believed - although not proven beyond the shadow of a doubt that adding aspirin to the water when planting will enhance the ability of plants to cope with drought as well as disease resistance. "The basic premise is that salicylic acid (the original active ingredient in aspirin) triggers plants to activate their version of an immune system, leading to an improved ability to fight off disease and fend off stresses like drought or cold." 
4.Dusting the roots with mychorizzae is another well advised option when planting. Mychorizae are a naturally occurring beneficial fungi that attach themselves to plant roots creating a symbiotic relationship.
Mychorizae penetrate the root systems of most plants in nature. They are helpful in providing improved uptake of water and nutrients from the soil. They help protect the roots from harmful pathogens and disease and help to reduce the effects of mineral Build Up on plants.
Benefits of Mycorrhiza
Enhanced Nutrients Absorption.
Increased drought resistance.
Increased pathogen resistance.
Enhanced plant health and vigor.
Trichoderma is another beneficial fungus that colonizes root systems. They prevent harmful fungi from entering the same root system, stimulate root development, and improve the plant's adaptability to environmental stress.
5. Silicon is proven to enhance drought and heat tolerance in plants. Silicon is a very abundant natural element that is present in all soil, in fact it comprises nearly 1/4 of the Earths Crust.
There are a number of ways to supplement the silicon your garden will receive via nature. Most common is via fertilizers that contain silicon dioxide and or silica. Another method is via foliar sprays applied to the foliage periodically. Foliar sprays of soluble silicon are effective for control of aphids and other sucking insects on many plants, they can also enhance the drought tolerance of the plants.
There are a number of ways to supplement the silicon your garden will receive via nature. Most common is via fertilizers that contain silicon dioxide and or silica.
Another method is via foliar sprays applied to the foliage periodically. Foliar sprays of soluble silicon are effective for control of aphids and other sucking insects on many plants, they can also enhance the drought tolerance of the plants.
Diatomaceous earth is comprised of large amounts of amorphous silicon dioxide and sometimes low levels crystalline silicon dioxide. It is a natural substance used for pest suppression and is also useful if amended modestly into the soil in that it adds silicon for absorption by the plants.
Footnotes1. SCIENTIFIC SUBSTANTIATION FOR THE INTRODUCTION, ON ROMANIAN TERRITORY, OF Lycium barbarum L.: A SPECIES WITH SANOGENE
2. Aspirin water for plant disease? Penn Live
3. Application of silicon enhanced drought tolerance in Sorghum bicolor