I don't see how a discount would attract people who are looking for what is let's face it a luxury product.
I'd be looking for different marketing strategies, mostly ones which as PP have pointed out will all take time to build up.
Build up contacts with teachers. Be sensitive to the way you are effectively encroaching on their territory and try and get them inside.
If you have any contacts with teachers, you could discretely ask around for recommendations for poor but deserving cases of pupils who deserve a boost but cannot afford a tutor to give free lessons to in return for favourable reviews and a reference.
Start a social media presence asking a daily question aimed at your target market. Engage with a one who responds and offer them 'first session free'. Advertise advertise advertise with a different 'offering' in different markets
Offer an early adopter a no upfront costs and payment only after the child has done well in mocks
Write yourself a business plan of how long you can afford to invest in starting up the business before it has to start generating income for you.
Any tutors round us seem to be snapped up pretty quickly so don't despise simple ads alongside the more complicated ones. Good luck.