As noted for the 1d (1/-), most known uses of these two Hospital Charity stamps are on philatelic covers.
Examples of the covers together with a listing of known covers are included:
St. Kilda to South Yarra and tied with a St. Kilda duplex with barred numeral 78.
1d local letter rate overfranked by 1½d on a philatelic cover.
Cover to Armadale and tied two strikes of an UPTRAIN/MG 15/Victoria framed Travelling Post Office cds.
Maybe a 1d local letter rate overfranked by 1½d on a philatelic cover.
Listing of the known covers with a single franking of the 2½d (2/6) stamp.
Multiple franking of the 2½d (2/6) on cover.
Mornington 113 to Broken Hill, NSW
Two singles overpaying the inter-colonial rate.
Provenance: Corinphila May 2018 Lot 3483.
South Yarra to Stuttgart, Germany
Pair of the 2½d (2/6) stamp tied by Numeral '200' duplexes of South Yarra.
8d foreign registered letter rate, 2nd step. Use of a 3d Registered envelope to Germany
uprated with a 1897 Charity 2½d pair tied by 'R' within a circle.
The cover has backstamps of Melbourne and Stuttgart.
Provenance: Millennium Auctions August 2004 Lot 208.
Millennium Auctions Rarities October 2004 Lot 65.

Franked by a pair of the 2½d (2/6) brown paying the 5d registered intra-colonial rate to Stawell.
Same address and handwriting as on a cover shown elsewhere with a 2½d (2/-) pair and a ½d green.
Intra-colonial letter rate: 2d;
Very late usage.
Provenance: Matthew Bennett February 2003 Lot 578;
Millennium April 2003, Lot 657.
Prestige Philately Sale 156 June 2010 Lot 688.
These are the only three covers recorded with a multiple of the 2½d (2/6) Brown stamp from the 1897 Victorian Charities issue.
Prestige Philately, May 2012, sale 173, Lot 733.
Millennium Auctions Rarities October 2004 Lot 65.
Combination and mixed franking of the 2½d (2/6) on cover.
A combination franking on cover from Melbourne Registered to Ronneburg, Germany. Two singles of the 1d (1/-) blue and a single of the 2½d (2/6) stamp mixed with a 1d orange Naish design on a plain cover.
Provenence: Millennium Auctions August 2004 Lot 208.
Millennium Auctions Rarities October 2004 Lot 65.
See elsewhere for a listing of the 1d (1/-) multiples used on cover.
Many covers were "artificially treated" to give the impression they were genuine. Sometimes original stamps would be soaked off and a Charity stamp affixed and "cancelled".
Also the cancellation on the ½d green is clear of the Charity stamp which may be covering a space previously occupied by another stamp.
In the example shown here and in the detailed scan below, it is clear that the two cancellations are of different format and size.