First off, congratulations for thinking about a getting your niece a gift which will be far more valuable than any toy. I regularly buy shares for my children / nieces / nephews to hopefully teach them (and their parents) investing.
One options is stock, out right. For minors, this is usually through an "informal" trust. So the name on the share certificate would be "Mark R. Smith in trust for Child T. Smith."
There are many different ways to accomplish this, for both Canadian and U.S. stocks, and each way offers different costs and lengths of time to complete. Until age of majority, taxes are attributed to the parent. DRIPing comes into play for longterm growth if applicable to the company.
RESP is great scenario as well. Ideally, the parent would have opened one already and you could give the cash to the parent to add to the account.
Free grant money from the Gov't is a no brainer, and any minimal risk is insignificant so long as the money isn't used in a group RESP plan.
The list of qualifying program is quite broad so too me that really isn't much a risk.