It is one of my favourite reserves and birding is great, but you will need lots of patience. Karoo birding is tough but very rewarding if you are patient.
In the reserve there are enough roads to drive along to look for birds without a 4x4. Karoo Long-billed Lark, Karoo Scrub-Robin and Karoo Chat is common. Dusky Sunbird and Cape Penduline-tit can be picked up along the main entry road by listening to their calls. As a matter of fact, knowing the calls of the Karoo birds is mega important! Layard's Tit-Babbler (beware confusion with the more common Chestnut-vented cousin) is also present. Look especially along gullies for this special. Keep an eye out for the nomadic Black-eared Sparrowlark, Double-banded Courser and Karoo Korhaan on the drive to the picnic spot.
The picnic spot is good for Southern Tchagra.
The boardwalk is good for Namaqua Warbler, but check out reeds near waterways such as at the bird hide for it as well. The drive up the mountain (excellent road) is great and at the top Grey Tit, Pale-winged Starling, African Rock Pipit and Ground Woodpecker can all be found.
The camping ground is a hotspot for birds - White-throated Canary, Fairy Flycatcher, African Red-eyed Bulbul and Pririt Batis.
If you have more time to your disposal the drive up the Molteno pass outside the reserve is highly recommended. It is an excellent birding drive and hosts most Karoo National Park specials including Black Harrier, Booted Eagle, Lanner Falcon, Verreaux's Eagle, Rufous-chested Sparrowhawk, Cinnamon-breasted Warbler, Sickle-winged Chat and further along the much sought after Karoo Eremomela.
Beaufort West dam is great for Black-necked Grebe and the plains to east of Beaufort is superb for Ludwig's Bustard, Namaqua Sandgrouse (also common along Prince Albert drive later afternoon), Double-banded Courser and Tractrac chat.
This is a brief overview. If you want more detailed info, just let me know.