I've got an engineering background and have taught computer aided design and programming in the past. I've taught statistics to classes largely composed of psychology students a few times as well.
Know what they are expected to know: the prerequisites for the course I've taught are very minimal so I can fully expect some students to struggle with basic algebra. While the majority do seem to be able to 'plug and chug' reasonably well, their ability to actually understand what the equations they're using mean conceptually is severely lacking.
Focus on what the math is saying: the first couple times I was able to cram a lot of different statistical analyses into a semester, and the students were largely able to keep up with the math and work out the solutions correctly. Unfortunately some of the really basic concepts still sounded foreign to them because they had spent all their time doing math problems.
Think small: If you start with probability and normal distributions it's a stretch to even progress through Z and t tests into the analysis of variance (if that's the sort of route you're taking) in a single semester. I think it's better that students more fully understand a couple, extremely basic types of statistical analysis instead of quickly being 'exposed to' several in the course of a semester. If one fully understands the logic and mathematical relationships behind a simple Z test on a sample mean they should be able to fairly quickly understand the more complex analyses.
If it is germane to the course, focusing on the non-math concepts like experimental design is also important, and generally more useful for students heading toward graduate school.