Okay, I'll need some clarification to answer this properly, but I'll provide a brief explanation of options below, as well.
Firstly, when you say , "I want to have a front-end option for users to enter such a post," do you mean that you want users to enter the post just like you would any other post, through the /wp-admin/ area? Or do you mean that you want them to actually submit the posts from the website, not in the admin area?
If the second option is what you're looking for and you don't mind paying for a wonderful plug-in that you can use on many projects, I'd recommend Gravity Forms. It has a built in section for creating forms that users can submit posts to through the front end, and with a little code hooking into the plug-in (and it has tons of action hooks to use) you can make it post to pretty much any post-type/taxonomy option.
If Gravity Forms isn't in the budget, you should be able to just create a custom page template with your form and when processing it submit the post to the posts table.
If you're looking more for the first, when you define the custom post type, there should pretty much already be an admin area section for the user to create/edit posts. If you haven't found this to be the case, please share the code you used and I'll try to figure out why it isn't working.
I would have made this a comment, but I can't do that yet, so if you could provide some more insight into what you are looking for, I'd be happy to expand on the information I provided and help you narrow down an appropriate solution.