Dollar weed is a wetland plant indicating that the area is very wet. Cut back on irrigation, or if this is a low area that remains wet, choose a different plant as perennial peanut does not like wet locations.
The University of Florida does recommend mowing weeds (just above the foliage of the perennial peanut) as a means of weed control. This helps to prevent the weeds from out-competing the perennial peanut for light. It is possible to spot treat weeds with a glyphosate-based herbicide like Roundup, but since these types of products are non-selective, they will also kill the perennial peanut in the treated spot.
See this fact sheet for more information on establishment and care of perennial peanut:
http://edis.ifas.ufl.edu/ep135
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