Is there a BC equivalent to the Ontario Trillium Benefits and Ontario Senior Homeowners Property Tax Grant or a deduction for rent paid in BC?

Sorry, BC has none of these credits available on your tax return. If you are eligible for the GST/HST Credit, you should qualify for the BC Low Income Climate Action Tax Credit, and this credit will automatically be applied for when you file your tax return. You will receive it at the same time as any GST/HST Credits.