Convincing your landlord to replace the carpet in your apartment can be as simple as asking or as drawn out and difficult as withholding rent. The level of difficulty will depend on your landlord and the type of tenant you have been in the past. Why the carpet needs replaced may also come into play. If you ruined the carpet, the landlord may have the right to expect you to pay for the new carpet. It is always best to be a good and dependable tenant for when these situations arise.
Pay your rent in full and on time every month. In most cases, landlords have multiple rental units, and successfully managing rental properties is a very demanding job. Landlords are more likely to do extra things for the tenants who pay their rent than the tenants who don't or are consistently late.
Ask nicely. Nobody, including a landlord, likes people to be demanding. Explain to your landlord why you would like new carpeting.
If your landlord provides maintenance request forms, fill one out and turn it in. If you talk to your landlord, give her a call during appropriate business hours and ask if she would be willing to look at your carpet.
Threaten to move. This won't always work, but if you are a good tenant and pay your rent on time and in full every month your landlord will not want to lose you as a tenant. Telling the landlord that you are willing to look for a nicer place and move might motivate him to replace the carpet.
Go to your county courthouse and ask to pay your rent in escrow. Only do this if your landlord said she would install new carpet and then does not, or if the landlord refuses to replace the carpet when it is clearly unclean or a tripping hazard. When you pay your rent to the court the money is held until the conditions are met. As long as the payments are still made on time every month the landlord cannot evict you for non-payment of rent.
Don't be demanding right off. Asking nicely can go a long way.
Keep in mind that if you push and get on your landlord's bad side, he might look for reasons to evict you.