Advice from a life-styler: Spanking is probably NOT the type of play for you if she's trying to hide the activity from her husband. I mean, technically, you could do it without marks/bruises, but it would have to be so soft that neither of you would enjoy it.
The reality is that a first-time spankee will typically tend to mark/bruise. The same holds true with someone who hasn't had a spanking for a long period of time, even if they were a heavy player before.
I echo the idea about Arnica (available at Whole Foods), but you'd probably want her on a regular regimen of sublingual (under the tongue/pill) Arnica for a couple of weeks before you play so that she is less likely to mark/bruise in the first place. Arnica cream will make the marks/bruises go away faster over the next few days, but not instantaneously. Or do both.
You can also minimize the chances of marks/bruises by making sure she's properly hydrated (drinking water before and after), including plenty of warm-up and cool-down (i.e., caress/stroke the area to make the blood flow toward the skin before and after spanking), and building up in intensity of the spanking (i.e., use the 1 to 10 pain scale system, asking her to give a particular spank a number on that scale, starting at 1 and stopping if she gives you a 7 or 8 -- if you want no marks/bruising, might even have to stop at a 4 or 5). Spanking through clothing instead of on bare skin is also a better way to minimize marks/bruises. If you weren't already planning to do so, start by spanking her through her dress or pants, then through just her panties (have her wear the ones with a full back, not a thong) and THEN move on to bare skin.
You probably already know this, but in case you don't . . . Find the tail bone before you spank and consider putting your hand over it. You do not want to spank this area ever. Stay at least an inch or two below the tail bone. Remember that the inner thighs and meaty backs of the thighs are also fair game as a spanking area. Most players don't realize that's an additional option. Avoid outer thighs because of the hip bones.