Well, for centerfire (not .45) there's quite a few options from Pardini and Benelli and the like, essentially their .22 target pistols scaled up to .32 S&W long.
If you're looking for a .45 gun or something you can run for both .45 and Centerfire, there's the 945 as mentioned and the Sig P220 X5/X6, both of which have the inherent mechanical accuracy you need for Bullseye, quality sights, and good triggers. However, I'm not sure how friendly they'd be to shooting offhand, and I don't think anyone makes adjustable palm shelf purpose-built offhand bullseye grips for either, even Nill or Rink. And there's the GT45, as mentioned earlier.
1911s are really the best for this application, though. What do you have against them that you're not willing to give them a try when they are so clearly favored? It would be by far the cheaper way to go, too. With the non-1911 guns mentioned in this thread, you're looking at $1500+ before you start getting reasonable bullseye qualities from the gun, whereas a ~$700 1911 can be perfectly serviceable for a new shooter. It'll take a while for a shooter's skill to develop the point that they see any real benefit from a super-tuned trigger or <4 MOA accuracy, and I'm guessing that if you're wondering if an HK would make a good bullseye gun, you're pretty new to the sport. With a cheaper gun, you're not out as much money if you decide bullseye is not your thing, and if you decide it is, by the time your skill merits a new gun you will have put so many rounds through the old one that the price of the gun is inconsequential.
