Is there a perek of tehilim that is particularly apropos to daven for someone else's spiritual growth (particularly in Torah learning)?
DailyTehillim.com suggests the tehillim to say for before learning Torah is:
Presumably, these pesukim would not only help those who wish to learn Torah themselves but also those who you daven for to be able to learn Torah as well.
There is Psalms 41 which could be applied to the situation:
Happy is he that considereth the underprivileged; the LORD will deliver him in the day of evil.
The LORD preserve him, and keep him alive, let him be called happy in the land; and deliver not Thou him unto the greed of his enemies.
The LORD support him upon the bed of illness; mayest Thou turn all his lying down in his sickness.