For just about any DSLRs out there, the pre-DSLR age lenses would provide the manual aperture setting you seek. For example, using a Canon-specific 3rd-party adapter, mounting FD and FL series lenses will work just fine. That's the good news. From what I've read, bird photographers frequently purchase an older, manual (FD/FL) long telephoto (400mm and longer), and use that on their DSLRs as the cost of an EF series long telephoto is just to pricey for most hobby photographers.
Setting shutter speed will still have to be done using a wheel of your choice on the DSLR. I don't know if all brands and models allow modifying which wheel does what, but using the one on the top of the body near the shutter release is usually the best position.
The bad news is that the older lenses do not have focusing motors inside of them, and must be manually focused using the appropriate ring on the lens. The problem is determining when the lens is accurately focused, as there is no split-ring or other image focusing capability visible in the view finder. There are after-market DSLR focusing products that solve that problem. However, using 'live mode' where the image is shown on the LCD on the back of the camera, one can do a pretty good job of focusing. The difficulty of using the LCD image to focus with is that it is too small too determine if it's exactly as desired or the subject is slightly out of focus, necessitating multiple 'close enough' focus shots. Even with new lenses and DSLRs, sometimes manual focusing is required when there is insufficient light and/or contrast for the camera to automatically focus. I've resorted to 'bracket' focusing in these situations twisting the focus ring in 'stops' either side of where I generally focused the subject. Like using exposure bracketing, the goal is to get one or two just-right images out of 8-10 shots.