By tournament:

1891 Rockhampton [4 July]

The list may be subject to change if more rugby union sevens tournaments are discovered.

Rockhampton

The 30 June 1891 advert for rugby by the Central Queensland Rugby Union in the Rockhampton Morning Bulletin promised a rugby union match between The Banks versus The Civil Service. Also on the bill was a Seven a side competition. The advert was placed by the CQRU Acting Honorary Secretary C. A. Mathias. Admission was 1 shilling; those with horse or buggy 2 shilling; and women received free entry to the enclosure. The matches were to be played at the Union Ground at Rockhampton’s Cambridge Street.

https://trove.nla.gov.au/newspaper/article/52347037?searchTerm=rugby%20%22seven%20a%20side%22&searchLimits=sortby=dateAsc

The advert was a Charity event for local hospitals and was also placed in the Daily Northern Argus on the same date.

https://trove.nla.gov.au/newspaper/article/213477749?searchTerm=rugby%20%22seven%20a%20side%22&searchLimits=sortby=dateAsc

The report of the match and the Sevens tournament was in the Daily Northern Argus of 6 July 1891. The report of the Argus is fairly circumspect of the notion of Sevens:- it notes that Sevens have been popular in ‘England’ (sic) under the auspices of the ‘English Rugby Union’ (sic). The journalist evidently not making the obvious distinction instead that Sevens were popular in Scotland under the auspices of the Scottish Rugby Union; and not aware that Sevens tournaments were actively frowned on by the English Rugby Union.

The first Sevens match was the Wanderers versus the Waratahs, which the Wanderers won. The Wanderers then played the Berserkers. Dusk was falling and the journalist writes that no-one could tell what the score was – but in any case the match was stopped as one of the Berserkers fell ill with the Wanderers well in the lead.

https://trove.nla.gov.au/newspaper/article/213346865?searchTerm=rugby%20%22seven%20a%20side%22&searchLimits=sortby=dateAsc