I think the problem is that cron is going to run your scripts in a "bare" environment, so your DJANGO_SETTINGS_MODULE is likely undefined. You may want to wrap this up in a shell script that first defines DJANGO_SETTINGS_MODULE
Something like this:
#!/bin/bash
export DJANGO_SETTINGS_MODULE=myproject.settings
/path/to/project/myapp/manage.py mycommand
Make it executable (chmod +x) and then set up cron to run the script instead.
Edit
I also wanted to say that you can "modularize" this concept a little bit and make it such that your script accepts the manage commands as arguments.
#!/bin/bash
export DJANGO_SETTINGS_MODULE=myproject.settings
/path/to/project/myapp/manage.py ${*}
Now, your cron job can simply pass "mycommand" or any other manage.py command you want to run from a cron job.