You can use plumbing commands.
Get your current HEAD, get the tree from there then your blobs.
Once you have the blob you can put the content in a textbox. When it's finished you just have to hash the new blob, create the new tree, the new commit and tadaam. It's "pushed".
PS: Remember you're in a bare repository, so check that every command you use don't need the index nor the working directory.
As it has been asked here is a step by step example.
First we get the current file content:
> git cat-file -p HEAD:var/test/text.txt
test
We do our little modification on that content and now have a new content ready to be pushed.
To save that content we're going to hash it:
> git hash-object -t blob -w var/test/text.txt
9764d221e6b50063b83c0268544c5d5b745ec9c5
This will save it, and return a sha-1 of that object (blob), the very next step consist in creating a new folder test which will contain our text.txt file. But first let's look at what does the current test folder look like:
> git ls-tree HEAD:var/test
100644 blob 9daeafb9864cf43055ae93beb0afd6c7d144bfa4 text.txt
So what we want to do here, is replace the previous SHA-1 (9daeafb...) with the new one (9764d22...) and generate a new tree based on that (pay attention to the \t).
> echo -e "100644 blob 9764d221e6b50063b83c0268544c5d5b745ec9c5\ttext.txt" | git mktree
b7788f9e8e9a24be31188167a6a0bc1de9e41d24
Great, so now we have the new file text.txt and the parent folder test, we now need var.
> git ls-tree HEAD:var
040000 tree 9bfb857f532d280ecd7704beb40a2ea4ba332f5a test
> echo -e "040000 tree b7788f9e8e9a24be31188167a6a0bc1de9e41d24\ttest" | git mktree
536f33626a47138499fade7df6d02327f75d80be
and now we need the parent of var (which is the root of our repository):
> git ls-tree HEAD
040000 tree 31a6ee5e7d14a0569721632a05234185a109d6bd var
> echo -e "040000 tree 536f33626a47138499fade7df6d02327f75d80be\tvar" | git mktree
7db3d6bc14cce98ff89ccc285b9d17965f5ca92b
And it's done, our tree is ready. The only thing missing is the actual commit:
> git commit-tree -p HEAD -m "commit message" 7db3d6bc14cce98ff89ccc285b9d17965f5ca92b
4aa2de2cf9e3e4f5470bcd1ee1e83ef6e4025eaf
But it isn't ready yet, now we want the commit to be the HEAD, so the very last step is:
> git update-ref HEAD 4aa2de2cf9e3e4f5470bcd1ee1e83ef6e4025eaf
And now we're done.
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