I do not think you can do this without being confrontational. That is, I think you have to have a face to face discussion with the line manager pointing out the inequality and asking for fair treatment. Try to present your case as logically and calmly as you can and if you get the same old 'no money in the budget' reply, say that, regardless of financial constraints, you cannot understand why your colleague receives more favourable treatment than you . Try to keep hitting the manager with your complaint of inequality and do not be tempted to argue with him/her about the firm's budget. The firm's budget is a red herring, the issue is inequality of treatment. Keep calm, nothing will be gained if you lose your temper.
Good luck.