Is there a Thaniyan for the Perumal and Thayar that can be recited at workplaces or public areas? Also, is there a specific shloka I should recite to remain a Deergha Sumangali (a woman whose husband is alive for a longer period)? 

To answer your request for a prayer for the Perumal and Thayar to be recited in public or workplaces, you can recite the first two shlokas of the Yathiraja Saptathi:

kampyAdyaM guruM vandE

kamalAgruhamEdhinam |

pravaktA cchndasAM vaktA

pancarAtrasya yaH svayam || (1)

sahadharmacarIM shaurEH

sammantritajagaddhitAM |

anugrahamayIM vandE

nityamagyAtanigrahAm || (2)

The following shloka is to be recited to remain a Deergha Sumangali (wishing for the long life of the husband)

kanyE dugdhOdanvatastAvakInaM manyE rUpaM mangalaM mangalAnAm |

yatsAvarNyaprAptabhadrA haridrA saumAngalyaM saMvidhattE vadhUnAm ||