Ah, Jungle Japes! This stage has been around since the Melee days; I still remember nodding my head to the beat of the DK Rap. But enough reminiscing from me, on to the point.
I'm not surprised people are counter picking this level against a fellow DeDeDe user, the short and choppy platforms work well in deterring chain grabbing, so you'll have to either rely on back throws for damage, or down throw to forward tilt. And the incredibly high ceiling makes killing with the up tilt pretty hard if your opponent can DI well.
One thing I find myself doing whenever I catch my opponent on one of the smaller platforms is either back throwing for 16% fresh, or down throw to forward tilt. In both cases, you should be throwing them away from the stage in attempt to set up your edge guard. Back air or forward air as you please since the up tilt takes a bit more time to kill then that of other stages. You wont be killing with up tilt until about the 130s - 160s depending on character weight.
This counter pick isn't absolutely horrid for DeDeDe, he does have a few tricks. If your CGing across the main platform at low percents, forward throw. Why you ask? Sometimes your opponent will hit the edge of the smaller platform, popping them back up into a bad position. Punish as you please.
Another trick I've learned is that attempting to swallowcide can be very beneficial if you do it on the left side of the stage, small platform. Upon landing in the water with D3's gut full, they'll automatically break out of your stomach and be in the swimming position. The current is usually strong enough for an insured kill, since this is unknown to most people. Beware that the current can take you under as well, so traverse these waters cautiously. Mash your jump button of choice immediately upon landing in the the river, your stocks are at risk.
Hope this helps.