What is your definition of "trails"? Gravel/railroad type trails? Light single track? Rocky, rooty, muddy?
I like the Schwalbe Hurricane. It has a smooth center section for good rolling on the road, but some knobs on the side for traction on looser surfaces. If you air them down when you're off-road, they do really well. They're available in a 40-622 (similar to your original 38-622 tires), and are also available in a 50-622 (also marked 29x2"). I have the 50mm versions on my Roam, and they do really well. They should fit your DS no problem.
If you want more aggressive than that, try the WTB Nanos. Those, too, are available in a few sizes that will fit your DS, including a 40-622 and a 52-622 (also marked 29x2.1"). Depending on what model year your DS is, these may have plenty of room or may be a very tight fit. The newer DS frames have more clearance than the older ones do. My dad has a 2015 8.4 DS and the 52mm Nanos just BARELY fit. The 40mm versions would be a safer bet.
Another option, if you want to try a larger tire, is the Vittoria Mezcal. They're available in a 52mm / 2.1" size. Again, these might be tight, but would give you good tire volume.
I have all three of these tires, in various sizes, on a few of my bikes. I'd say the Schwalbe Hurricanes are the smoothest, and softest/most compliant, followed closely by the Vittoria Mezcals. The Mezcals have very good grip off road; I have a lot of confidence on those. The WTB Nanos are a little rougher on road, though also very nice off road. I don't have as much trail time on these as I do the Mezcals, but they seem very nice, and are highly acclaimed.