DipTrace can, it's a bit of a fiddle to draw the pad design directly in DipTrace itself, but you can import a DXF to make it easier.
This is how I make offset hole pads, but the shape can be anything (closed, obviously).
http://imgur.com/a/eCnD3
Very nice!
Be warned though, sometimes DipTrace goes crazy when exporting polygons with a large number of points (when you convert to pad it pulls it in as a poly). This can cause your fab to have troubles when they try to process the Gerbers.
As an example, last week I created 3-way solder jumper. I wanted the outer pads to have rounded edges, so here's how I did it: I created a new pad, set the type to poly and then edited the points. I let it create a 360 point polygon, which was a circle! Then I deleted 180 of the points, leaving me a half circle. Finally, I added a few points to extend the square side.
It came out beautifully! Unfortunately, during export, DipTrace turned those ~180 points into *thousands* of operations in the Gerber. OSHPark couldn't process it. So I ended up just using square pads. :-/
I think I can fix the problem though... If you ever zoom in on a normal round pad in DipTrace, you can see it's not perfectly round; there's aliasing because they're using a limited number of points to create the circle. So, I suspect if I go back and do the half circle again, but start out with 36 points instead of 360, it'll export just fine.
And to the OP: You might also look into a took like PCB Librarian. It'll let you create footprints and custom pads, then export them to pretty much any tool you want.