I think so too. Just checking - this is for births during or after 1837? Thanks
Civil Registration began in the third quarter of 1837. Depending on when the children were born I'd choose one as far away from the start of registration (preferably one with as uncommon a first name as possible to narrow it down) as it took a good while for registration of births to catch on with a lot of people. I can't remember the figures but at first there was a high percentage of births which weren't registered.
If there are multiple choices in the index, I'd email the registrar (not sure if those registers would be held by Durham (Bishop Auckland) or Gateshead and explain, depending on how busy they are they may check the registers for you to find one which matches the criteria you give them (Dad's first and surname, Mum's first name is all you are sure of).
Both Durham and Gateshead Registrars have online search facilities, if you can find their local reference for the registration that will help them find the entry you'd like checked.
Boo