Click where you want your transport to move too, and then while it's moving click on a unit to unload, this works for me.
I'm not sure if there is an automatic way of doing it or not.
gaming.stackexchange.com/users/2285/Viper_Sb
I believe Viper_Sb's answer is correct for EXACTLY what you are asking for, but I believe this is worth mentioning: You can do something similar by ordering the transport to drop all units (D?) and then holding the shift key to queue up a move order.
The transport will move on as soon as it is empty.
EDIT
: See Raven Dreamer's comment on Viper_Sb's answer for more details.
He is faster at composing than I am!
gaming.stackexchange.com/users/1410/WillfulWizard
Okay!
You can easily replicate this behavior either manually or with waypoints.
Manual Method:
Order the dropship to move somewhere.
When the medivac is above the desired location, click the unit's silhouette to unload them mid-flight.
The move order for the medivac won't be cancelled, but the unit will unload.
Waypoint Method:
Order the dropship to move where you want to unload the unit in question.
Shift-click on the unit's silhouette to queue an unload command.
Then shift-click another location to queue a second move order for your medivac.
This will result in your medivac moving, dropping the unit(s), and continuing to move all in a single, smooth action (i.e., no loss of speed due to deceleration).
You can also queue the "unload all" command this way, though that will cause the dropship to stop momentarily.
gaming.stackexchange.com/users/336/Raven Dreamer
I came here for this exact question and as I mess around with the replies I have discovered an improvement on what has been offered.
By improvement
I mean less keystrokes and the method is very easy to transfer to multiple drops at once.
The trick is that instead of clicking on the silhouette of each unit you can simply click unload all and target the transport itself!!!
Additionally the waypointing already mentioned above can be used to queue the entire process up.
Will multiple transports
you just need to target all transports with the unload all action.
Here is an example, If we have 3 overlords full of roaches and want to drop them all in the enemies base, we would like to start dropping as soon as we cross into the enemy base and keep moving to drop the subsequent units further into the base.
The keystokes are as follows: Move, Shift + (d, Lclick@overlord1, Lclick@overlord2, Lclick@overlord3, Rclick, Rclick@ground)
Translated
this would tell your overlord to move into the edge of the enemy base, you then hold shift to queue your actions, d selects the "unload all" command and you have to left click all 3 overlords, followed by a right click to cancel the unload all cursor and
finally another right click on the ground where you wish your overlords to move to (further in the base).
I am going to go ladder and see how my opponent likes 3 perfectly executed drops going off all over their bases at once =
D.
gaming.stackexchange.com/users/9409/Jbigg
It took me 2 years to understand it.
Basically, let's say you have 3 overlords.
You load up your units into the overlords.
You press D and hold D and select a place to move.
While holding D and overlords are moving, you click on an overlord.
At this time the overload automatically drops everything inside with 1 click.
So the trick is to hold the D button and make them move somewhere.
When you click on the overlord it will auto-unload, and you can change the direction of the path that the overlord is taking.
In summary, if you press D, you hold D, and if you click on an overlord it auto-unloads, if you click on the ground it moves there (and it drops everything if you click on the overlord itself).
gaming.stackexchange.com/users/46704/How to drop LIKE A BOSS
I've seen players drop units from overlords/medivacs while the transport was still moving, but I can't figure out how to do that myself.   If I order the transport to unload all and then issue another move command, he stops unloading... what's the trick?
How do I drop units from overlords/medivacs while the transport is still moving?
gaming.stackexchange.com
<starcraft-2>
gaming.stackexchange.com/questions/7400
gaming.stackexchange.com/users/1863/Dfowj
Press D and hold it, and if you click on an overlord it auto-unloads.  There are two ways, one you can click on the unit to unload while its moving and two you can press and hold D and click on the ground in order for it to move there. 
User suggests clicking on the unit to unload while its moving. User suggestions pressing and holding D and clicking on the ground in order for it to move there.