Are they viewing them in a browser? Some web browsers are not very good at displaying true colours of photographic because they do not read the ICC colour profiles that are embedded in then. If the images are being processed in Photoshop, make sure the artists are using the sRGB color space rather than Adobe RGB, and that they are not embedding color profiles.
Along the same lines as Linda's suggestion: Take a look at the color profile of the image sent to you by the artist before you work on it. If it's anything other than sRGB, convert it. If you're on a Mac, you can use the Info panel (Command-I) to quickly check for a color profile on a graphic; otherwise, you can fire up Photoshop and use its Info panel. To convert the color profile within Photoshop, use Edit > Convert to Profile, which will preserve the image appearance but attach a different ICC profile.
Fireworks doesn't acknowledge color profiles (at least FW8 doesn't), so when you open the image in FW, you might see a small color shift. When you save or export the graphic from FW, the ICC profile may be stripped from the file. If it's important that it be preserved, as a final step, you could try re-opening the exported graphic in Photoshop and re-assigning the sRGB profile (using Edit > Assign Profile) before sending it off to your client. Some web browsers do observe color profiles now—Safari and Firefox, for instance. I think it's good to include them for photographs, but they shouldn't really be necessary for web or interface graphics.
Here's a related post that might be helpful:
Thank you both for your responses. You were correct. I checked with the person who sent me the image, and he's using Nikon software that appears to utilize the Adobe system. The file was indeed saved as Adobe RGB--not sRGB. He was able to save it with an sRGB profile. When I opened the new image in Fireworks and exported it, it looked the same as the original.
I could not find anything in Fireworks CS5 that would tell me anything about color profiles which is too bad. It would be really nice if there was at least a warning.