Back to the machine knit soakers/longies. I prefer shorts or longie style because they were never worn as daywear, and I think wool soakers are a bit much to wear under pants, and I just couldn't get a good fit on Meg with traditional soakers. Just by extending the legs a little, they became shorts, which are also better at dealing with diaper blowouts.
This is a sketch of what the machine knit longies look like before sewing up. Hopefully you can click on the picture to make it bigger. I'll go through it set by step.

Make a large swatch and wash it. Yes. Or else you won't know what will happen to the soaker when you wash it! Figure out your row and stitch gauge, and measure your baby over their diaper...waist, hips, thighs, rise (front and back). Figure out how many to cast on (you don't need much ease over the diaper, but a little is good).
Use waste yarn and an open cast on and cast on. Knit for about an inch using just a slightly tighter gauge, then decide how you want the fold of the casing to be...picot edge? garter edge? nothing requiring extra work? Work your turn row, then switch to the 'real' tension/gauge and knit the same number of rows as the first half of the casing.
Pick up the open stitches of the cast on, remove the waste yarn and using a larger tension (ie T9 instead of T5, or KP4 instead of 3), knit one row to 'seal' the casing.
Knit another inch at the main tension. Now, we're going to do some short rows to raise up the back waistband. The short rows will be in the middle section only, which is the back 'bum'. I find it helpful to mark on the needlebed where the side edges (hip) will be. The middle bum in '0' and the center front seam is what ever your outer stitch is, so the hip 'seam' is halfway between. So, if you casted on 100 sts, from 50L to 50R, the hip 'seams' are at 25L and 25R.
If the carriage is on the left, put all the stitches from the hip seam to the right edge in hold/D position (all the way forward). Knit across. You need to take the yarn under the first needle in hold position (the one next to the one in working position) and bring it back up between the first two needles in hold position (make sure it stays in the carriage). This is just like 'wrapping' a short row in handknitting. Now, put the same needles in hold on the other side--from the hip seam out to the edge--and knit across, again wrapping the first hold position needle that you came to. 

Now...you can get fancy and do math, or just eyeball it. It's a diaper cover! Just eyeball! You want to do about 1 to 2 inches worth of short rows, what is your row gauge? You've already done two rows, so subtract those. How many short rows are now needed? How many sts do you have in work position (hint--half of what you cast on, as we're working on the backside only now). You want to work short rows so you put in hold about 1/3 of the needles on each side of the backside. I mark this on the needlebed too. So, the back side is 25L-0-25R, so that means 1/3 of that is about 16sts. I'd work short rows until you have 16 more needles out of work on each side, and 18 needles in work in the middle. If you want 10 more rows, you will put 2 needles out of work on the side opposite the carriage before knitting across, but on a few of the rows, just do one needle out of work. So, a bit of math, a bit of eyeballing :)
(If you need help with short rows, just holler, or look for Diana Sullivan's videos on YouTube).
After doing the short rows, put the needles in hold, back into work, on the side opposite the carriage, and go slowly across. Repeat for the other side. Then continue to knit straight until you get to about 2" above where the crotch seam will be. Here, I do short rows again, but I do them like a wedge...
After doing the short rows, put the needles in hold, back into work, on the side opposite the carriage, and go slowly across. Repeat for the other side. Then continue to knit straight until you get to about 2" above where the crotch seam will be. Here, I do short rows again, but I do them like a wedge...
Start like the earlier short rows, and when you get down to 1/3 sts in work, instead of knitting all the way across, do increasing short rows by putting 2 or 3 or 4 or 5 needles back into work on the side opposite the carriage. Again, you're making a diaper cover, not a wedding dress. Finish off by knitting to the length required (it's easier to measure along the front seam, but good idea to check the center back too. You can take it off on waste yarn or just do your best on the machine...or, if you had done the swatch and know your row gauge...)

Now, to work one leg at a time. Cast off, on the side next to the carriage, one inch (a little less for small sizes). This is "A" on the sketch. Put the needles on the far side of 0 to hold/D, but keep in work "A" on the other side of 0.
What this means is, if the carriage is on the right, cast off one inch; let's say that's 5 sts. Still going with our 100st example, put all the sts to the left side of 0 into hold position, except 5L-0. Knit across (you'll knit from 45R to 5L). Now, cast off that one inch of sts that was on the far side of 0 (L5-L1), as well as another one inch worth continuing in the same direction (R1-R5). This means, now that our carriage is on the left, cast off 5L-0-5R then knit across. You'll now be working on 6R-45R.
Work the leg for the length you want. Or, take the yarn you have left and split it in two even balls, and work till you have a few yards left for seaming. You can rib the bottom, do seed stitch, garter stitch, let it roll, whatever. You'll need to add claw weights to the side that's in hold position.
To make other leg, have carriage on left, and cast off "A". You should now have 45L-6L in work. Finish this leg like the other one!
I'm sure this all seems very wordy and complicated. Just go step by step, and remember...it's a diaper cover! And, it's made quickly, so you can rip it back, re-knit, and still be done faster than if you handknit it!
Let me know if you need more info!
I know that's not a great picture. This is the side used for measuring rows (you can tell by the "R"). You place the bottom of the ruler on the bottom of the first row of main colour after doing the 2 contrast rows. Where the next set of contrast rows meets the ruler, you read the number that's on the ruler. And it tells you--without any math--how many rows are in 4", even though all you did was knit 60 rows! The other side of the ruler is used for stitches, and you place it along the row of the two marked sts, and it tells you, based on the 40sts, how many sts are in 4". Cool! For this sweater, I got 26st and I forget how many rows, LOL.