Is there a depreciation schedule for carpet when the carpet is new
when they move in but is ruined and unusable when they move out?  How
much can I deduct from their security deposit

Laws vary from place to place. I doubt that this question is
answerable without knowing the city/state/nation in which the rental
property is located.

You're actually asking two different question. One is a tax question
(carpet depreciation), and the other is a landlording question. Now,
I'm neither a lawyer nor an accountant; you should consider checking
with one or both.

As for depreciation, IRS Publication 527 allows a 5 year depreciation
using a General Depreciation System. See
http://www.irs.gov/publications/p527/ar02.html. However, there's also
the issue of whether the carpeting is a capital improvement or a
repair; you depreciate the former and expense the latter.

However, your real question seems to deal with tenants who ruined your
carpeting. The first place to look is in your lease. Does your lease
address this? If it specifically does, then there's your answer. If
it's silent on the matter, then the reasonable/fair/defensible thing
to do is to take the depreciated value of the carpet and subtract all
cleaning and repair costs from that. If the carpet is ruined and must
be replaced, then (barring language to the contrary in your lease) you
could charge them for depreciated value. For example, if the carpeting
cost $1,000 new....5 year depreciation ($200 per year)...and the
carpet is 3 years old, then the depreciated value of the carpet is
$400. If cleaning and repair costs are $300, you could deduct $300
from their security deposit. If the carpet is ruined and must be
replaced, you could deduct $400, even though the new carpet might cost
$1,000.