There are several problems with this idea:-
Good deeds planned by one party do not bring reconciliation: The very fact that you want to do good deeds shows that you acknowledge your guilt - your offense is not against the molecules that make up this universe - but against God - a person. Reconciliation is therefore what is needed. For reconciliation, it is not enough that you think of something nice and do it - you need to find out what God requires! Analogy: If I broke your watch, it would be appropriate for me to ask you: "What would you like me to do? Shall I get it repaired? Or shall I buy you a new one?" - it would not be appropriate for me to think: "Okay, since I've done something bad I'll make amends by doing something good - fix dinner for him maybe".
Good deeds cannot "balance" the bad we've done because they are our duty anyway - not something "extra" (see Mark 12:28-31). It works the same way in civil law. If you’re on trial for murder, you cannot argue saying, “What about all the people I’ve been nice to? I’ve murdered one person, but have been nice to more than one person, so I should be set free!”. When Indian actor Sanjay Dutt (see image) was on trial for illegally possessing arms in a case linked to the 1993 serial blasts in Mumbai, he argued for a reduction in his sentence citing his charitable activities. The judge did not comply. Do you think God will reduce your sentence because you have done some good deeds? When the laws of an infinitely holy God confront sinful people like you and me, there is only one result: awful curse and condemnation (Galatians 3:10).
Our good deeds are not good enough: When we sin, the breach between us and God (who is infinitely holy), is infinite, and it cannot be bridged by our finite good deeds. Thus, even if it were possible for us to do something really good - something out of the way or "extra", it would still not be enough. The wages of sin is death (Romans 6:23) - infinite suffering and separation from God - not community service. Analogy: Imagine you wake up to find yourself naked in the president's office. What will you do? The "atheist" approach is to deny the existence of the president and the shamefulness of nudity. The "religious" approach is to prepare for the arrival of the president - hold a newspaper around yourself. Unfortunately, newspaper clad persons will get kicked out by the security guards just like nude persons will! Our good deeds are as pathetic as that newspaper wrap! But just imagine the president's son shows up and offers you a designer suit - purchased at great cost but free for you - yours if you accept your helpless condition and submit to the president! This is akin to what God has done for you.
God does not find our good deeds "good": Think of a person who has a sore in his hand from which pus and blood is oozing out. He offers you food held in his hands. How does it look? That's how your good deeds look to God - as sinners we are like rotting lepers in His sight. Our best deeds are filthy rags in God's sight (Isaiah 64:6). There’s no way we can win His approval. In spite of all this (tears fill my eyes as I write this - how merciful of God to even bother about sinners like us!!), God has still made it possible for us to reach Him
Conclusion: Your good deeds do not change the logical outcome of the fact that you have sinned against an infinitely holy God! There is only one way out!