If your goal is to avoid annoying people who feel strongly that parts constitute a whole, and a whole comprises parts, then it would be better to say
The application site consists of an existing care home that comprises 59 bedrooms and 85 registered bed spaces.
than to say (as in the original)
The application site comprises an existing care home which has 59 bedrooms and 85 registered bed spaces.
Having said that, I must say that I am very sympathetic to Brian Donovan's example (in a comment above):
Modern Texas comprises the entirety of the pre-contact Karankawa territory.
and DJ Far's further example (also in a comment):
The city of San Francisco comprises the county of San Francisco.
I consulted a number of books on English usage, however, and only one of them addresses the question of using comprise in connection with one (singular) thing encompassing of another (singular) thing—although Webster's Dictionary of American Usage (1989) notes this example of (formally) plural-to-plural comprising in Jane Austin, Mansfield Park (1814):
Three months comprised thirteen weeks.
The exception to the general, narrow focus on the (deplored) application of comprise in situations where compose, constitute, consist (of), or make up are just as clear and less controversial, is in Eric Partridge, Usage and Abusage (1947), which provides the following discussion:
comprise and constitute. Comprise, 'to constitute, to compose' is rare and , I think, to be avoided, as in 'Ten dogs comprise the pack'. Whereas constitute = 'to form, to make up', as in 'Reading, writing, and arithmetic ... do not in themselves constitute an education' (Lubbock), comprise = 'to include', esp. in a treatise; 'to sum up' (e.g., 'to comprise much in a short speech'); 'to comprehend or include under or in a class or denomination'; (of a thing) 'to contain as parts forming the whole; to consist of (certain specified parts)', as in 'The house comprises box-room, nine bedrooms, bath-room, etc.'; and 'to embrace as its contents, matter, or subject', as in 'The word politics ... comprises, in itself, a difficult study' (Dickens) (The O.E.D.)
Partridge's commentary seems to permit "Thing 1 comprises thing 2 consisting of x, y, and z" if you interpret thing 2 as being "embraced as to its contents, matter, or subject."
Still, it is remarkable that authorities from Fowler, Modern English Usage (1926), to Evans & Evans, A Dictionary of Contemporary American Usage (1957), to Follett, Modern American Usage (1966), to Bernstein, The Careful Writer (1973), to Shaw, Dictionary of Problem Words & Expressions (1975), to Room, The Penguin Dictionary of Confusibles (1979), to Copperud, American Usage & Style: The Consensus (1980) to Claiborne, Saying What You Mean (1986), to Randall, Webster's New World Guide to Current American Usage (1988), to WDEU (1989), to Wilson, The Columbia Guide to Standard American Usage (1993), to O'Conner, Woe Is I (1996), to Wallraff, Word Court (2000), to Bryson, Bryson's Dictionary of Troublesome Words (2002), to Garner, Garner's Modern American Usage, second edition (2003)—despite discussing whether parts can comprise a whole—have nothing to say on the precise question that the poster asks here.