Bridgend council wants to limit kerbside rubbish collections to save money and hit Welsh government targets.
There are currently no restrictions on the number of black bags each household can put out.
A council spokeswoman said it was exploring use of different colour bags to show if the rules had been broken.
The changes, which will also include the start of a nappy and sanitary item disposal service, will be introduced in April 2017.
Councillors will discuss the changes during a meeting of the cabinet on Tuesday when the new seven year contract for waste collection will be awarded.
A report by the council in March said it was predicted to fall short of the Welsh government 58% target for recycling - meaning it could be fined at Â£200 per tonne.
The two bag restriction would mean it reaches 64% by 2019-2020, it predicted.
Under the new system the council may issue a roll of specifically branded bags to each household, at the cost of about Â£147,300 a year.
Residents who break the rules could have their waste left at the kerbside, their addresses could be recorded and they may be visited at home.
Residents in Bridgend county borough will only be able to throw away two black bin bags of household rubbish a fortnight under council changes.