There may be easier ways, but one way is as follows:

Check the Levy court tax records of Sussex County Delaware (found in the Delaware Archives) for the years 1830 till 1840 something. Eventually you will find your Peter Wilson coming of age (21), and making his contribution to society. The questions you want to ask yourself are:
1) In which hundred did he come of age?
2) Are there indications in the record telling me who's his father? (example-- Peter Wilson of Tho--Thomas that is; or Peter Wilson of Cha--Charles that is...)
3) Do I see his 'father' in the same hundred? If the record indicates an "of ___", than look for that man to be in the same hundred. If there is only one of other Wilson listed in the same hundred, they probably won't indicate "of___" because your not distinguishing between two or more male adults, and therefore indicate who this young new tax payors' father is. Usually new tax payors where listed at the end of the alphabetized list of names. So, with Peter, I'd look in particular at the year 1837 at the end of all the 'W's listed in each hundred. He would have turned 21 that year, and listed as stated at the end. Unless Peter owned property prior to age 21, he wouldn't be listed in the record as a head of house.
4) Look at all the levy court tax records you can in the time frame of when Peter lived in Sussex. Sometimes you get good info when not expecting it. Also, the levy court tax records are divided up with overseers "road tax", delinquent property tax, summary levy court tax lists, individual overseers levy tax record, ect.. Anything that says 'levy court' during the pertinent years you'll want to look at.
5) Compare your findings with the census records from 1810, 1820, 1830, and 1840. This helps you eliminate potential 'fathers'.