Many producers get frustrated dealing with artists who constantly ask for free beats. It's time to turn that frustration around and turn it into an opportunity.
There are many reasons why artists ask for free beats, maybe because they haven't got any money at that point in time, maybe because they don't see the value in paying for beats, or maybe they think they are too good to pay for beats, they should just get everything free (yea right, too good huh, Jay-Z pays for beats, you better than him?). Whatever the reason, accept the fact that their understanding may not be the same as yours, and you shouldn't get disheartened.
What you must not do is let the opportunity pass, as just because their financial situation or understanding is at that point right now, it doesn't mean it will be like that forever, and if you let them go, you'll never find out!
What you should do is create a relationship with them, and you do that by saying "sure, you can have a free beat, just join my newsletter for helpful and valuable information and you also get a free beat too". Now, you probably don't want to word it like that, but you get the gist of it. So you create a page on your website with a mailing list sign up form and direct any artists who want free beats to this page where they can sign up and get a free beat delivered to their email address. As long as you keep in regular contact with your subscribers (offering valuable advice to them, not just a bombardment of sales emails and beat special offers), then you will be in the forefront of their mind and when they are ready to buy beats, they will almost certainly come to you because you've been a valuable source of information to them over the weeks/months/years.
But I don't want to give away a free beat!
Well you don't have to, but it does help seeing as that is what they're looking for, so it's a very good incentive for them to sign up. If you don't want to give a free beat then there must be another good incentive for them to sign up. It can be anything from "top 10 recording tips for the perfect rap vocals" to "how to write lyrics to blow your audience away", whatever it may be, make it valuable. Share your experience and knowledge in the industry and you will be rewarded.