Is there a way to allow a user to create their own password in a runtime solution?

One way I've used is to create a separate "Passwords" file containing fields for userID and password. Then have the main file open to a screen where the user has to "sign in". After that, script to check to make sure the userID matches the password, and then set a global field to allow access to whatever layouts, etc., the user is entitled to.

It ain't perfect, and it's a bit kludgy, but it can work, especially if the layouts can't be accessed except through buttons.

But FM client can access that file. It is down to design.

In your heading you talk about user chosen passwords, but in the actual question you use instead the word create.

If you create a number of passwords in a file, then bind it to create a runtime, you can allow users who log in with each of the passwords you've created to change the password to one of their own choosing. For each password you create, you can select to enable or disable the "Allow user to change password" option.

A user will exercise this privilege (if you have granted it for the password they have used to open the file) via the File > Change Password... command. If you have not granted the privilege, the "Change Password..." command will be grayed out

Thus a runtime can acquire passwords which are chosen/set by the user (and which replace passwords originally set there by you). If desired, you can include a redundant set of extra passwords which can lie dormant, to be called into play should the user discover a need for extra points of access.

If you want users to be able to add additional passwords beyond those you've coded into the file before binding, then it would be necessary to consider alternative methods along the lines of those suggested by danjacoby and Anatoli.