Use Conditional Formatting.
Date at start of range in A1.
Date at end of range in A2.
Cells to change color - A3 to K3
Start by selecting A3:K3, then
<Format> <Conditional Formatting>
Expand the first box, and change to "Formula Is"
Then enter this formula in the next box:
=AND(A3>=$A$1,A3<=$A$2)
Then click on "Format", and select your formats,
Then <OK> <OK>.
Enter your start and end dates in A1 and A2, and you should be done.