Yes, you can give discounts by customizing your members' plan.
As soon as you confirm a membership, the first invoice is generated, so the best time to give a discount for any new members is before you confirm them. There are two ways to do this:
1) To customize a plan so that all new members signing up to it receive the discount, go to Setup > Plans > Edit plan > Extras > Add Extra. You can create a negative charge so that it is applied ongoing as a separate line item on your members' invoice and deducted from the plan total.
Setting up the discount as an extra as opposed to discounting the plan price directly under Basic Settings has the added benefit of the member seeing how much a full membership costs.
2) To add a discount for just one member, as opposed to all new members signing up for that plan, click on 'Allow to customize the conditions before confirming the membership' when you add the new member.
To add a discount to an existing member's plan, go to their Member Profile > Plan > Customize Plan and make any changes you would like. Be sure to click on 'Save Plan' afterwards. Any changes will be effective immediately.