The amendment is one of a number of changes to the bill that the organisation has tabled through Liberal Democrat peer Lord Kirkwood, and cross-bencher Baroness Meacher.
The bill is currently going through committee stage in the Lords, and represents the government's latest attempt at getting more people off benefits and into work.
Child poverty campaigners have criticised it in the past for suggesting that Jobcentre Plus advisors may have the final say when finding suitable childcare for a parent who has the opportunity to return to work.
Kate Green, chief executive of CPAG, said members of the House of Lords have a tremendous opportunity to improve a flawed bill.
"By safeguarding full parental choice on childcare, making high quality, tailored support a positive entitlement and giving lone parents a premium as an incentive to engage in work related activity, the bill will be significantly improved and more likely to succeed," she added.
