Why not just do a web search for motels in Morris or Benson?  There can't be too many motels in either city.  I did a quick web search and found the Best Northland Prairie Inn in Morris.  They allow pets for $15/night.  There has to be some mom & pop motels that would allow dogs.  I think a little time searching the web and making a few calls will get you what you need.  Or maybe someone on this site is from the Morris/Benson area.  Good luck.