Hi Mary thank you for your question. You are perfectly correct, a diamond shape cartouche is called a "lozenge" however there are so many diamond shape jewelry marks!
John Cook (New York, NY, USA) - ca 1868 - 1880s) had a trademark very similar to what you've described, two diamond shapes side by side with a C in one diamond.
If you have a Jewelers Loupe or a magnifying glass with at least 10x magnification try to identify what the other letter is in the other diamond shape.
