To help speed breeding you can create spontaneous conception AND birth!
Just drag a female breeder onto a male and as soon as you see "going indoors", just tap on "detail" and check if she is nursing. If so, just drag her on the screen and POP!, she's holding a baby! If you don't get the "going indoors" message or she isn't nursing when you check, just keep dragging her to other males or even back to the same one until you do. Even if the males run away I just keep dragging them back and dragging the breeder to them. It's kinda weird to create such a forced breeding program. I keep thinking to myself "get back there and make a baby NOW!"

Also, if the breeder is weakened you won't get the nursing message but you can just move her after the going indoors message and see if a baby pops up immediately.