In Canada we have a regulation that looks like this:
Canadian Aviation Regulations 2011-1
Standard 625 APPENDIX A - ELEMENTARY WORK
The following list is exhaustive; if a task is not listed, it is not elementary work. Elementary work is a form of maintenance that is not subject to a maintenance release. Hence, it need not be performed by a holder of an AME licence, or by persons working under an AMO certificate. The owner is responsible for controlling authorizations to persons who may perform elementary work.
<snip>
(14) repair of upholstery, trim and cabin furnishings;
I looked at the FARs but didn't see something similar. Canada tends to be stricter than the US, but in this case, if the FARs have no similar provision, we are privileged. I have snipped an extensive list of stuff the private owner can do.
Note: AME means Aircraft Maintenance Engineer, the rough equivalent of an A&P-IA. AMO is Approved Maintenance Organization, similar to an FAA-Approved Repair Station.
Dan