Offer to pay for copies, and ask if they will accept a gratuity for their search. Remember that they are doing you a favor. The records they have are not public, but private business records that they are allowing you to access. Never volunteer to search through their records yourself. Many funeral directors have found that their records can be put in total disarray by others going through them.
Most funeral homes have a list of pall bearers, but the registure book is given to the family.
Most do not keep a copy of the death certificate. Thirty years ago, the records can be very sparse. If you are writing to a funeral home, be specific about who you are looking up and include dates. Be specific about the information you are looking for. If it is only the name of the cemetary, let them know.