Hi everyone,
I was trying to make a template of k2 content module for my front page. What I did is to copy /modules/mod_k2_content to/templates/mytemplate/html/mod_k2_content, and then under "tmpl" folder, I created a folder named "frontpage" and copied modified default.php into it. But, on module creating screen, in sub-template selection, there was only 1 option other than "use default", which is tmpl. So, I created a folder named "frontpage" at the same level as tmpl, this time, I can select "frontpage" template, only to found out it didn't work. After tried several different locations to upload default.php, I finally tried uploading it to the orignial place, which is /modules/mod_k2_content/tmpl/Default/, and select "tmpl" sub-template on module creating screen. This time, it worked. Please be noted I could still see the "frontpage" option there.
So as a conclusion, I think this could be a bug. Although I have copied those module files as instructed, the module wouldn't accept it and kept using the original files.

afterwards, I tried the following: I deleted all the files under html folder, now for sub-template there is only 1 option - Use Default. I created a "frontpage" folder in /modules/mod_k2_content, but there is still only Use Default option. Then I created a "front" folder in /modules/mod_k2_content/tmpl/, and copied default.php into it, this time I can choose sub-template as front and everything goes well.
So at least there is a problem where the "where to find sub-templet" rule is not consistent. In /modules/mod_k2_content/ the sub-template is to be found under tmpl folder, while in mytemplate/html/, the sub-template is to be found at the same level as tmpl folder and the module considers tmpl as a template.

No one can answer this or I didn't descripe the issue clearly?

Try
Creating a directory yoursiteroot/templates/html/mod_k2_content
copy the dir siteroot/modules/mod_k2_content/tmpl/default to the newly created folder under html dir
make a copy of default called MyMODK2 in the same folder
Trick is to skip the tmpl folder