Yes. We are capable of performing good deeds. Unregenerate people perform good deeds all of the time. The wealthy give to charities. Families adopt orphans. Parents love their children and children return that love. Some attend church, tithe regularly, are kind, generous, loving, helpful people. They do good deeds. Their actions are honorable.
But what does Scripture say about this? Take a look at Isaiah. Here we will find a clear answer to the question.
We have all become like one who is unclean, and all our righteous deeds are like a polluted garment. We all fade like a leaf, and our iniquities, like the wind, take us away. (Isa 64:6)At first glance this verse is often misunderstood. There is an emphasis put on the inability of man to perform any good works. But does the verse say this? I think it does and it doesn't. It does say that we are incapable of performing any good deed that will cover up any of our sinfulness. It also says that all of our good deeds are like a polluted garment. Our righteous deeds are like bandages that cover our leprosy, and covering our leprosy they become polluted.
But does this mean that there are no good deeds performed?
No. It means that righteous deeds have been performed, and yet those righteous deeds are tainted by our own sinfulness. You see, the problem is not that we commit sins. The problem is that we are sinners. In other words, the problem is not that we get things dirty, we are dirty. And we need to be cleansed from our sin nature, and then the 'getting things dirty' problem will be taken care of.
This is the reason we are to be clothed in Christ. Christ does not simply cover our sinful 'leprosy', He cleanses our sin.
This leads to another question. What about Christians who do good deeds? Are those good deeds polluted with our sin?
I do not believe that the good works performed by Christians are tainted by their sin. Since it is God working through us and producing fruit in us, those works are not tainted by sin. They are what we were created for.
For we are his workmanship, created in Christ Jesus for good works, which God prepared beforehand, that we should walk in them. (Eph 2:10)
What about Christians who sin? All Christians are to be daily repenting of their sins and Christ is daily cleansing us from our sins. This is known as sanctification. And sanctification is the process by which we are being saved from our sins. Our hope (expectation) is that one day we will be thoroughly cleansed from our sin (glorification) and look upon the glory of God in the face of Christ.
Soli Deo Gloria