Someone posted a request earlier today for a method of making trunnion pockets on a drill press with emphasis on getting them truly opposite each other. The post seems to have disappeared (at least I can't find it anymore) but here goes anyway.
This is basically my setup. Now obviously it is on a milling machine, not a drill press, but bear with me. There are two important features about this setup for locating trunnion pockets. First, the barrel is held between centers so it is perpendicular to the spindle. Second, it is held in an indexing device to allow it to be rotated exactly 180°. You will note the generous use of short pieces of 2x4 and bar clamps. These are there to add clamping power to the lathe dog and indexer to prevent rotation of the barrel while the machining is going on.
Now let's transpose this setup onto a drill press (dp). Since the dp doesn't have an adjustable table (and the adjustable tables that can be had for dp's aren't very rigid so I don't recommend using them for this), we will need to mount the holding devices to something that can be slid around on the dp table to align the barrel with the spindle. I would get a adequately long piece of 2x6 that is both straight and flat and a couple of pieces of 4x6 at least 6" long (these dimensions are assuming a barrel of about 4" maximum diameter; a smaller one could use a smaller jig.) One piece will hold your dead center, the other an adjustable (for length) center. They need to be drilled through for 8" long 3/8" lag bolts. The holes need to be the same distance from one edge, say 4.5", and of sufficient diameter that the threads on the bolts will be engaged. It would be a good idea to put 60° points on the threaded ends of bolts to the minor diameter of the threads. Glue and screw one piece of 4x6 with lag screw to one end of the 2x6. The other piece needs to be located such that the barrel will fit between it and the previously anchored one. I would generously apply drywall screws but no glue as you may want to use this on barrels of differing length. Make sure the screw points are at the same height from the bottom of the 2x6; if they aren't, shim the second piece of 4x6 (or sand it thinner) until they are. If you don't, the trunnions will not be perpendicular to the bore.
The other issue is to get the pockets on truly opposite sides of the barrel. Presuming you have welding capability, I would lightly weld a piece of 1/2x1" steel about 4" long to the barrel in a place that can be easily repaired when you take this piece off. Assuming the barrel at this time has no features that require a particular orientation of the trunnions, it doesn't matter where the 4" piece is located. We are going to use it as a reference plane and the trunnions are going to be located parallel to it. The barrel will be located be applying a square to the 4" piece such that it is perpendicular to the table and parallel to the spindle. Securely clamp the barrel in position on the jig to prevent rotation. Measure the diameter of the barrel at the center of the trunnions. Divide this number by two. The following part of the procedure requires more than two hands. Place a square on the upper flat of the jig against the side of the barrel at the trunnnion centerline and measure from the square the radius of the barrel as above determined. Put an accurately located center punch mark there. Using a wiggler in the dp chuck, center the center punch mark under the spindle and clamp the jig to the dp table securely. (I'm not much of a wiggler user myself; I think you will have to put the wiggler in the punch mark with the spindle turned off, then raise the spindle and turn on the machine at low RPM looking for the wiggler to be swinging around. You need to move the jigged barrel such that the wiggler doesn't move after it is lifted.)
You are now ready to drill. It is a good idea to set the depth stop so you don't accidentally drill into the bore. After you have drilled the first pocket, loosen the anti-rotation clamps and rotate the barrel, aligning it with the square on the opposite side. Apply the clamps again and drill the other pocket.
Now, having written all of that, I think you need to remember that the pockets need to be flat bottomed and a twist drill has a 118° point. So you should regrind your drill to a flat bottom and redrill after roughing out most of the material with a regular drill. This is going to cause some extra vibration as the drill is not now set up to remove metal efficiently, so be careful.
After you have finished the pockets, remove the welded on piece and clean up the spots where the welds were.
It would be possible to make a jig using V-blocks instead of centers but that requires calculations and accurately made/measured V-blocks (because of the usual taper of a barrel) to get the bore horizontal.