I've been on the receiving side of "no ability to promote", and ultimately the best thing a manager can do in that situation is to have an honest conversation about what is and isn't possible.

In addition, don't just give up. Keep talking and helping out. It could be advice on how to stay motivated or at least not demotivated, carving out space for interesting projects or developing new skills, or even helping that person find a new opportunity outside the company.

Dealing with unmotivated unproductive people you have limited ability to actually manage is beyond my experience.