Coreopsis and Roundup

[Hay Dude]

Hello plant lovers. My wife and I planted lots of coreopsis around our house. The life cycle begins in spring and flowers most of the summer, then dies off in fall, as you well know. In winter, we are left with small weeds that grow over top of where the coreopsis was. We think it competes with the coreopsis for water and sunlight, hindering its growth. Attached is a current (March 14th) picture of the weeds with their familiar tiny white flowers.
My question is, can I spray these weeds NOW, while the coreopsis is dormant, killing the weeds without hurting the coreopsis? Last thing I want to do is kill it. The weeds look awful, though.
Thanks for any help you may have.