Here is a very brief list of recommendations and blooming periods from a 1857 gardening manual.    While this is later than the Regency period by several years, it is still fairly accurate.  I have also included some notes from an 1809 gardening manual.

Please note that it lists the plant names and times as they were written in this book.  The names used are the Latin, but I have indicated the more common names, as well, where possible.  Latin should be used to identify species more accurately since the common names often mean different plants depending upon your country of origin, area of the country, or even which historical period is referenced.

Seasons:  Spring        Summer        Autumn

Spring

The spring list consists chiefly of bulbs and low-growing herbaceous plants which come into bloom from January to the middle of May.

Blue Crocuses, pale lilac Anemones, pale blue
Anemones, white Hyacinths, dark purple
Alyssum saxatile, yellow Crocuses, pale lilac
Ranunculuses, Turban, scarlet Crocuses, yellow
Heartsease, variegated Tulips, mixed, common, red, yellow and white
Tulips, Royal Standard, various colors Tulips, Gold Standard, red and yellow
Hyacinths, white Hyacinths, blue
Tulips, Duc Van Thol., scarlet and yellow Hyacinths, red
Crocuses, purple

Notes from 1809

March/April: Crocuses and snow-drops, as well as other common bulbs are blooming.  

May:  Hyacinths and tulips are now in flower.  Transplant the following tender annuals into their beds:  cockscomb, tricolors, balsams, globe-amaranthus, egg plants, and stranomiums.  Carnations plants in pots should be given the utmost care so they will grow with vigour.  Transplant the less tender or hardier flower plants:  the African and French marigold, chrysanthemums, the marvel of Peru, China aster, India-pink, ten-week stocks and the common kinds of balsams, the capiscums, mignonette, persicaria, cabiouses, and Chinese holly-hocks.  Transplant also:  columbines, sweet-williams, single scarlet lychnis, rose-campion, catch-fly, Canterbury bells, Greek valerian, tree-primrose, fox-gloves, French honeysuckles, and others.

June:  Transplant out the wall flowers, July-flowers, sweet-williams, carnations, pinks, and columbines which were sown in March or April.  Also, transplant hollyhocks, tree primrose, fox-gloves, Caterbury-bells, Greek valerian, single rose campion, rockets, scarlet-lychnis, and other perennial and biennial plants as were sown two or three months ago.  Carnations will, toward the latter end of this month, begin to break their outer cup or flower pod for flowering, but more generally not till July.

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Summer

The summer list consists chiefly of hardy annuals and biennials, which should be brought forward ready to plant the moment the bulbs have done flowering and are removed.  Most roses bloom in the period stretching from May through the the beginning of July.  A few varieties bloomed in the autumn.

Clintonia pulchella, blue (Blue-bead lily, Queen's cup) Erysimum Perowskianum, orange (Wallflower)
Clarkia pulchella alba, white (evening primrose family) Nolana atriplicifolia, blue
Godetia bifrons, pink and white Collinsia bicolor, pink and white
Yellow Wallflower, yellow Gilia tricolor alba, white
Nemophila insignis, bright blue Gilia tricolor, white and purple
Nemophila atomaria, white Nemophila insignis, blue
Leptosiphon densiflorus, pale purple Nemophila insignis, blue
Godetia Linleyana, rose and white Collinsia grandiflora, purple and blue
Schizopetalon Walkeri, white Nemophila phacelioides, pale blue
Clarkia elegans, lilac Collinsia bicolor, pink and white
Godetia rubicunda, purple Gilia tricolor alba, white
Clintonia pulchella, blue Clarkia pulchella, rose
Godetia rubicunda, purple Nolana prostrata, blue
Leptosiphon androsaceus, lilac Iberis umbellatus, purple
Godetia rosea alba, rose and white Collinsia verna, purple
Erysimum Perowskianum, orange Godetia Romanzovii, purple

Notes from 1809

July/August:  Gardens must be cared for and plants regulated as they bloom.

August:  Plant autumnal flowering bulbs, such as:  colchicums, autumnal narcissus, Guernsey lily, amaryllis, and autumn crocus.  Some will bloom in September, some in October.

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Autumn

The autumn list consists chiefly of greenhouse plants, such as Pelargoniums (geraniums), Verbenas, Lobelias, and so on.  A few roses bloomed in autumn, and this is typically when fruit and berries were harvested.

Verbena Melindres, scarlet Verbena Buistii, pale rose
Crucianella stylosa, flesh color Anagallis Monelli, blue
Verbena teucrioides carnea, flesh colour pelargonium, variegated ivy-leaved, variegated
Lobelia ramosa, blue Verbena ignea, scarlet
Lobelia bicolor, pale blue Campanula carpatica, blue
Verbena Hendersonii, purple Verbena Bishopia, pale purple
Pelargonium, Frogmore, scarlet Pelargonium, Cooper's, scarlet
Calceolaria rugosa, yellow Calceolaria integrifolia, yellow
Lobelia axillaris, pale blue Anagallis Phillipsii, blue
Petunia phoenicea, purple Petunia, Lady Peel, Purple
Verbena Barnesii, rose Verbena Marryattii, rose
Petunia hybrida, purple Senecio elegans pleno, purple
Heliotropium corymbosum, pale purple Heliotropium peruvianum, pale purple
Nierembergia filicaulis, lilac Oenothera macrocarpa, yellow
Oenothera Drummondii, yellow Verbena Tweedieana, scarlet
Nierembergia intermedia, purple Tournefortia heliotropioides, pale purple

Notes from 1809

September/October:  Colchicums, autumnal narcissus, Guernsey lily, amaryllis, and autumn crocus.  Some will bloom in September, some in October.  Hardy annuals such as marigolds and pelargoniums will continue to bloom, as will petunia.  Fall bloomers will also include asters.

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