I had to give up my first Parthian campaign. It just wasn't possible to defend Hatra and Kotais every year. Palmyra was Egyptian, Damaskus and Antioch were Seleucid and they kept attacking me in Hatra. Pontus, supported by the Seleucids, attacked Kotais frequently. I just didn't make eneough money at a certain point and my diplomats had either died or were bribed. No way of trading maps, retraining armies. You only can win so much battles when outnumbered, without retraining.
Inspired by Maltz' stories, I started over again.
I'll spare you the long story and just give you two tips.
I figured that to conquer quickly I needed more units than I had at Susa and Artaxarta (your capitol). I moved my general and the HA out of Campus Sakae and built a diplomat there. After two turns this diplomat met the Skythians and sold Campus Sakae to them. By this time my campus sakae army was already onboard the single ship you start with and on it's way to the capitol. It's important that Campus Sakae is empty when you want to sell it. Try to get a multi-round tribute from them. Next turn Campus Sakae revolted with 5 units East-Inf and 12 units of gold chevron peasants. I didn't expect this but was happy to have a little inf. garrison. The EastInf was shipped, the peasants disbanded because their upkeep is too expensive, Campus Sakae was sold again. To make it short, it happened two more times. After this northern army from Campus Sakae joined the middle army of Artaxarta, which had in the meantime taken the rebel town to the west, they moved against the Armenians.
I remember that Campus Sakae was particulary troublesome during my other campaign, as it is so far from anything, doesn't make enough money etc. I guess it was a good idea to get rid off it at the beginning but you may consider to do it only once to increase your forces by a loyalist rebellion.

My second tip considers the south. It's very easy and a good idea to take Seleucia in the second turn. But after that, try to take Palmyra as fast as possible before anyone else can. This has the effect that 1. Seleucia won't be attacked and 2. Palmyra is quite a comfortable base for a Cav-army. You can reach Damaskus and the bridge to Hatra in one turn. Antiochia, Hatra, Sidon and Jerusalem need only two turns. Reinforcements from Seleucia take three turns to reach Palmyra. And, it's a good territory to hire Bedouin Warriors.
From this base I try to conquer the 5 surrounding cities. So far I took Damaskus and destroyed almost all military opposition. Jerusalem has 2 units, Sidon 2, Antiochia has 4 and 6 in a fort while a full stack of Hoplites roams around Hatra. It helps to have at least 2 spies around Palmyra.
I think that once I've take Jerusalem and Antiochia, there won't be much left of the opposition.

R'as