Question
The second round of rose blooms have brownish color on them.  I don't see any Japanese Beetles, so what could be the problem?

Answer
There is a tiny insect called a thrip which sucks the juices out of the rose petals and in the area they have sucked on, it goes brown. It sounds like you may have these bugs. Also if you water and the water gets on the petals then some roses will go brown because the water causes the thin petals to rot. See if there is any tiny ( very tiny) insects on the rose and if there is then I would get a spray that is specifically for thrips.