The following parks offer camping, details are available at their websites (linked):

 

Bucks County

Nockamixon State Park 

Modern cabins, Hostel

Lake Towhee Park

Tinicum Park

Tohikcon Valley Park

Tent sites and cabins

 

Chester County

French Creek State Park 

Tent and electric sites and cabins, organized tent and cabin sites

Hibernia

Tent and RV, organized group sites

 

Delaware County

Ridley Creek State Park

Organized group sites only

 

Montgomery County

Evansburg State Park

Organized group sites only

Fort Washington State Park

Organized group sites only

Green Lane Park

Tent, organized group and equestrian sites