Rivers enters the fray following his cameo against Lancaster City last weekend, with Liddle option to choose himself to enter the line-up at the Microlise New Manor Ground.
The means James Harrison and Alex Nelson - who is suspended - both miss out on a place in the starting 11 for the clash with the Robins.
Shane Bland continues in goal, with Connor Smith, Frankie Whelan, Nathan McGinley and Aaron Haswell at the back, supplemented by manager Liddle who makes his second start of the campaign.
Harley Dawson retains his place after netting his first goal in the 2-1 Emirates FA Cup win at The Giant Axe, and features in the middle along with Adam Gell.
And former Darlington man Rivers is deployed with Donald Chimalilo in support of Matthew Tymon, who is rewarded with another start after a strong performance last Saturday.
Harrison drops to the bench along with midfielder Ronnie McGrath, while Callum Wilson and Jake Charles are also named.
Nick Cranston is the substitute goalkeeper.
Whitby Town: Shane Bland, Connor Smith, Aaron Haswell, Gary Liddle, Frankie Whelan, Nathan McGinley, Harley Dawson, Adam Gell, Matthew Tymon, Donald Chimalilo, Jarrett Rivers.
Substitutes: Callum Wilson, Ronnie McGrath, James Harrison, Jake Charles, Nick Cranston.