If you need their investment, negotiate based on it as an early investment rather than as a partnership (a partner gets lots of sweat equity and a pittance based on some small amount of cash invested--equity bought with cash is usually much smaller and on less favorable terms in the sense that small sums do not bring seats on the board, etc.). But you probably don't need that money. Buy back their share (if you've already incorporated and issued shares), and call it a friendship rather than a business partnership. You do not want to deal with these questions down the road when the company has assets.
I don't mean to be patronizing (I don't see how it remotely is). Going at something with a partner isn't a requirement for success, nor is it only for "cheering up." Investors like to invest to successful ventures, and a business partner is a nice assurance for them.
But go ahead and show 'em, you rebel without a cause. ;)