Keep them well filled, keep the heart rate high, and give them some combination of dobutamine and milrinone. Avoid high pulmonary arterial pressures.
The tricuspid valve is not one usually prone to isolated regurgitant failure, outside of Ebstein's anomaly or carcinoid syndrome. Rather, the reason it regurgitates is usually because the RV is grossly distended by the effects of pulmonary hypertension. The two problems rarely exist in isolation.
Isolated tricuspid regurgitation is usually well tolerated. The right ventricle can compensate for volume overload much better than it can compensate for pressure overload. It is the coexistence of pulmonary hypertension that makes this a problem.
Tricuspid regurgitation with pulmonary hypertension is a situation where increasing pulmonary pressure makes it easier for the right ventricle to eject blood backwards rather than forwards. Thus, whenever the pulmonary vascular resistance increases (eg. in hypoxia, or with high PEEP) the RV will decompensate and cardiac output will plummet. These people tend to react to recruitment manoeuvres with cardiac arrest.
Preload needs to be kept high. The pressure pushing back against the regurgitant jet is really your CVP, and so one needs to keep the CVP abnormally high in order to maintain forward flow through the right chambers. Venodilators such as GTN are to be avoided.
The heart rate needs to be kept high, around 90. The shorter the period of contraction, the less blood is ejected into the central venous circulation. Furthermore, a high heart rate means an increased cardiac output, which means a greater removal of venous blood from the central circulation, and less symptoms of peripheral congestion.
Well, these people are usually in AF anyway. You may not be able to do much about that. It certainly does not seem to be an issue of critical importance. Once definitely would not want to give contractility-impairing drugs to combat this AF.
Contractility of the right ventricle is all-important. The greater the contractility, the greater the contraction of the tricuspid annulus, and thus the regurgitation is decreased. Inotropes and chronotropes are desirable; milrinone is the natural choice.
Systemic afterload is meaningless, but pulmonary vascular resistance is very important, and should be kept as low as possible. Any pulmonary vascular resistance is an obstacle to forward flow, and will thus increase the regurgitant fraction. Pulmonary vasodilator properties of milrinone may play some role here.
Moore and Martin's chapter on valvular disease in "A Practical Approach to Cardiac Anaesthesia" is a must-read
(in general, that book is awesome)
Stiefel, Alexander, and Volker AW Kreye. "On the haemodynamic differences between sodium nitroprusside, nitroglycerin, and isosorbide nitrates." Naunyn-Schmiedeberg's archives of pharmacology 325.3 (1984): 270-274.