IMLS grant programs that fund collections care include:
Conservation Assessment Program, an IMLS program operated in conjunction with Heritage Preservation, that supports a 2-day site visit to your institution by a conservation professional.
Museums for America, the largest IMLS grant program for museums. Collections care proposals fall under the "Collections Stewardship" category.
Preservation Assistance Grants, a program of the National Endowment for the Humanities that helps small and mid-sized institutions improve their ability to preserve and care for their humanities collections.
The Funding for Collections Care section of the Guide to Online Resources.