Here is my trial, corrections and additions are welcome as usual:
rana jIti rAma rAu Aye
sAnuja sakala sasIya kusala Aju
avadha Ananda badhAye
Our King (rAu) rAma has won (jIti) in battle (raNa) and returned back (Aye) home. Together (sa) with his brothers (sakala anuja) and Devi Sita (sIya), all well (kusala), today (Aju) he has come back to ayodhya (avadha). Thus there are joyful (Ananda) celebrations (badhAye) all around!
[The reason why brotherS are mentioned instead of brother is beacuse even Sri Bharata did not reside in Ayodhya during the time of Sri Rama's exile, he resided in Nandigrama and only entered the city together with Sri Rama]
aripura jAri ujArI mAri ripu
vibudha subAsa basAye
He burnt down (jAri) [this in context of Hanuman ji burning Lanka] and annhilated (ujAri) the kingdom (pura) of the enemy (ari) and eventually killed (mAri) him (ripu). Consequently, he re-established (basAye) the devatAs (vibudha) on their respective planets (subAsa).
[Ravana had forcefully engaged all the devatas in his service and removed them from their residences, after ravana's death, the Lord re-established them back]
dharaNi dhenu mahideva sAdhu
saba ke saba soca nasAye
Thus, the Lord excavated (nasAye) all (saba) the worries (soca) of mother earth (dharaNi), the cows (dhenu), all (saba) the brahmins (mahideva) and the saints (sAdhu).
gayi lanka thira thape vibhishana
bacana piyUSa piyAye
He went(gayi) to lanka and firmly (thira) established (thape) vibhishaNa as the king and also rejuvenated him by providing him/making him drink (piyAye) his nectar-like (pIyUSa) words (bacana).
sudhA Sichi kapi kRpA nagara nara
nAri nihAri jiyAye
By showering them (sIchi) with ambrosia (sudhA) he gave life (jiyAye) to the monkey warriors (kapi), by giving them mercy (kRpA), he gave life to the men-folk (nara) of the city (nagara) and by his sidelong glances (nihAri), he gave life to the women-folk of the city!
[Accordingto rAmacaritamAnasa, when the war was over, the Lord asked King Indra to shower ambrosia on the dead monkey warriors and thus the dead monekys regained theor lives]
rAma rAja kula kAja sumangal
sabani sabai sukha pAye
In this auspicious (sumanga) traditional deed(kula kAja) of offering the kingdom to sri rAma (rAma rAja), everyone (sabani) gained (pAye) all (sabai) the happiness (sukha).
dehI asIsa bhUmisura pramudita
prajA pramoda baDHAye
The overjoyed (pramudita) brahmins (bhUmisura) offer (dehi) their blessings (asIsa) on the occassion, thus increasing (baDHAye) the delight (pramoda) of the citizens (prajA).
I cant get the last paragraph, let me try again, ill complete it soon. I must say - this was difficult! To bring out the correct emotions ........
needs some corrections.