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Go to your team's fixture list and there'll be a button in the main window that says "Arrange Friendly".
Click that and you're taken to a new screen. On the right-hand side there's a dropdown box that says by default "Choose...". Click on that then on "Choose Other...". Find the club you want to play, click on their team name to bring up their teamsheet, and at the bottom of your side-bar there should be an option to "Pick For Friendly". Click on that, et voila
Then try a team that isn't in a playable league. In my game that's an English team below Blue Square South/North.
Or let your assistant amanager arrange them in the future, it's a lot less hassle and occasionally he can get a big team to come who wouldn't if you tried to arrange it.
You can also arrange friendlies with the reserve and under 18 teams of any club. They usually have few if any matches during the pre-season and will even be available throughout the season.
I regularly arrange friendlies with the reserve sides of larger clubs to gain some quick money for my Cambridge City side.