In the 1851 census of Appleby (Derby part) there are 17 peqple with the Bird surname. Three in particular are descendants of mine ie Joseph Bird aged 69 years his wife Margaret aged 66 years and Richard Bird aged 66 years. It would seem they resided in Oakthorpe prior to Appleby and before that they resided in Packington and were baptised there. If anyone has any further information on please let me know.
I think that you must be referring to Joseph Bird bap. at Packington on 8 Dec 1782 and Richard Bird also bap. at Packington on 25 April 1785 - sons of William and Ann Bird. If so, then I think I can help.
William and Ann Bird had 9 children baptized at Packington. In addition to Joseph & Richard, these included: Thomas bap 25 Mar 1775 William bap 9 Nov 1776 and John bap 27 Dec 1786 I am descended from Thomas. Thomas, William and Richard were carpenters and Richard also kept a grocery shop at Packington. John became a farmer and is in the 1861 Census at Donisthorpe.
Their parents were William Bird and Ann Hill who married at Packington on 17 Aug 1773. According to the IGI Joseph Bird married Margaret Wayte at Ashby on 10 June 1806 and I have found the bapisms of 2 of their children: Thomas 15 Mar 1807 at Ashby and Richard 2 Feb 1817 at Stretton en le Field
If Joseph and Margaret were in Appleby in 1851, I suspect that they didn't stay there long, as the Leicestershire and Rutland burial index indicates that they were both buried at Donisthorpe: Joseph on 14 Mar 1852, aged 69, and Margaret on 8 Mar 1854, aged 67. In both cases the abode is given as Oakthorpe. Richard was buried on 15 Feb 1852 at Packington, aged 68
Their father - William Bird - was buried at Packington on 6 Mar 1827, aged 76, indicating a birth year of 1751. I have not yet discovered where he came from. However, a Thomas Bird was a witness at his marriage in 1773 and this was presumably a close relative. I have noticed that the Netherseal parish registers include entries for a William Bird baptized on 21 May 1749 and a Thomas Bird bapt on 5 Nov 1752 (both the sons of John Bird), so these look worth following up.
The mother - Ann Hill - was baptized at Packington on 28 Feb 1747/8 and was buried there on 25 June 1824, aged 76. Her parents were Thomas and Ann. According to the IGI, Thomas Hill married Ann Sharp at Packington on 9 Dec 1735. They are both buried at Packington and their grave stone can still be seen there. The inscription states that Thomas died on 1 Jan 1784, aged 69 and that Ann died on 28 Oct 1791, aged 76. The Hills appear to have been well established at Packington and the IGI suggests that Thomas' father was a Robert Hill bapt. there in 1682.
There appears to be some connection between the Birds of Oakthorp and Repton, but I don't yet understand how it came about. The 1861 Census for Repton shows a William Bird, widower and basket maker, aged 53, who was born at Oakthorpe. There is a son in the household, Thomas, aged 13, born at Oakthorpe and this seems to be almost certainly the Thomas that was baptized at Appleby in 1848.
The 1861 Census also shows a Richard Bird, blacksmith, aged 43 living at Repton. He was born at Moira and married Lydia Pegg on 23 June 1840 at Repton. A number of their children were born at Aylesbury, Bucks. I think it is possible that both William and Richard are sons of your Joseph Bird. However there was another Richard Bird, son of John and Elizabeth, who was baptized in Ashby in 1817 and I don't know whether the Repton blacksmith was the son of Joseph or John. Several of the Bird family became carriers on the canal and had wives and children born far afield.
Apologies for the length of this response, but I hope there is some information here that might be useful for you and other Bird researchers.