I just wanted to point out that there are a variety of shortcuts for the DP motion in SSF4.
First, I actually wouldn't recommend the down-forward, down-forward that Decency mentions since it actually relies on doing the motion slightly wrong. You can't do a DP with exactly two joystick motions. Why does it seem to work? It is hard to move straight to down-forward without having it also do forward or down first and that usually gives enough different inputs for it to come out. But if you do down-forward twice perfectly it actually won't work. Experiment in training mode with inputs on and will see what I mean. Having said that, here are some other options:
(Note: while in the normal motion usually you let the joystick go to neutral after the forward, none of the ones below need you go to neutral at any point)
forward, down-forward, forward: That should be a bit easier on a pad and is also helpful if you're already walking forward (just have to slide the joystick down and up slightly). You have to be careful not to go up so far that you jump but it is definitely doable. It is also the version you'd use with Ken to do a kara-dp.
down-forward, down, down-forward: This is IMO the most useful overall. It has the big advantage that you stay crouching throughout the motion. If you're trying to anti-air someone jumping in at you, it gives you more time to react since your body is lower (in older sf games without the shortcut, pro people would whiff a cr.kick so they could do the normal dp motion during the animation without standing the char standing up). It is also good during bnb combos like cr.lk, cr.lp > cr.lp xx h.dp. If you keep the joystick in down-forward as you do the start of the combo, you only have to slide the joystick over to down and back to down-foward and hit punch to cancel into the dp.
down-back, (slide to) down-forward, down, down-forward: If you happen to be crouch blocking already and need to do a dp suddenly, just slide over to down-forward and do the rest of the previous shortcut. It is harder since you have that extra slide motion in there which takes extra time but definitely is doable.
I'd still recommend generally keeping the stick in down-forward during a crouching combo if you're planning to do a dp or tatsu at the end. Feels a bit scary at first but if you drop a link and have hit the next button, they're going to be able to mash-punish as a counter-hit anyway (and if they don't then your moves will start being blocked and you can always move to down-back at that point). For combos that go up and down (say cr.lk, st.lp > cr.mk xx h.dp on Ken), the first part doesn't matter but when you do the cr.mk you should have the stick in down-forward so you can immediately slide over to down, down-foward and hit punch to cancel into a dp.